【数位dp】【动态规划】【KMP】1397. 找到所有好字符串

简介: 【数位dp】【动态规划】【KMP】1397. 找到所有好字符串

作者推荐

【动态规划】【字符串】【表达式】2019. 解出数学表达式的学生分数

本文涉及知识点

动态规划汇总

LeetCode1397. 找到所有好字符串

给你两个长度为 n 的字符串 s1 和 s2 ,以及一个字符串 evil 。请你返回 好字符串 的数目。

好字符串 的定义为:它的长度为 n ,字典序大于等于 s1 ,字典序小于等于 s2 ,且不包含 evil 为子字符串。

由于答案可能很大,请你返回答案对 10^9 + 7 取余的结果。

示例 1:

输入:n = 2, s1 = “aa”, s2 = “da”, evil = “b”

输出:51

解释:总共有 25 个以 ‘a’ 开头的好字符串:“aa”,“ac”,“ad”,…,“az”。还有 25 个以 ‘c’ 开头的好字符串:“ca”,“cc”,“cd”,…,“cz”。最后,还有一个以 ‘d’ 开头的好字符串:“da”。

示例 2:

输入:n = 8, s1 = “leetcode”, s2 = “leetgoes”, evil = “leet”

输出:0

解释:所有字典序大于等于 s1 且小于等于 s2 的字符串都以 evil 字符串 “leet” 开头。所以没有好字符串。

示例 3:

输入:n = 2, s1 = “gx”, s2 = “gz”, evil = “x”

输出:2

提示:

s1.length == n

s2.length == n

s1 <= s2

1 <= n <= 500

1 <= evil.length <= 50

所有字符串都只包含小写英文字母。

动态规划

直接利用封装好的数位模版,自定义状态 枚举串的后缀和evi的前缀 最长 部分。

之前的长度len,如果当前位相同,len+1。

否则,比较最长的前缀,类似KMP。

代码

核心代码

class KMP
{
public:
  virtual int Find(const string& s, const string& t)
  {
    CalLen(t);
    m_vSameLen.assign(s.length(), 0);
    for (int i1 = 0, j = 0; i1 < s.length(); )
    {
      for (; (j < t.length()) && (i1 + j < s.length()) && (s[i1 + j] == t[j]); j++);
      //i2 = i1 + j 此时s[i1,i2)和t[0,j)相等 s[i2]和t[j]不存在或相等
      m_vSameLen[i1] = j;
      //t[0,j)的结尾索引是j-1,所以最长公共前缀为m_vLen[j-1],简写为y 则t[0,y)等于t[j-y,j)等于s[i2-y,i2)
      if (0 == j)
      {
        i1++;
        continue;
      }
      const int i2 = i1 + j;
      j = m_vLen[j - 1];
      i1 = i2 - j;//i2不变
    }
    for (int i = 0; i < m_vSameLen.size(); i++)
    {//多余代码是为了增加可测试性
      if (t.length() == m_vSameLen[i])
      {
        return i;
      }
    }
    return -1;
  }
  vector<int> m_vSameLen;//m_vSame[i]记录 s[i...]和t[0...]最长公共前缀,增加可调试性
  static vector<int> Next(const string& s)
  {
    const int len = s.length();
    vector<int> vNext(len, -1);
    for (int i = 1; i < len; i++)
    {
      int next = vNext[i - 1];
      while ((-1 != next) && (s[next + 1] != s[i]))
      {
        next = vNext[next];
      }
      vNext[i] = next + (s[next + 1] == s[i]);
    }
    return vNext;
  }
protected:
  void CalLen(const string& str)
  {
    m_vLen.resize(str.length());
    for (int i = 1; i < str.length(); i++)
    {
      int next = m_vLen[i - 1];
      while (str[next] != str[i])
      {
        if (0 == next)
        {
          break;
        }
        next = m_vLen[0];
      }
      m_vLen[i] = next + (str[next] == str[i]);
    }
  }
  int m_c;
  vector<int> m_vLen;//m_vLen[i] 表示t[0,i]的最长公共前后缀 
};
template<int MOD = 1000000007>
class C1097Int
{
public:
  C1097Int(long long llData = 0) :m_iData(llData% MOD)
  {
  }
  C1097Int  operator+(const C1097Int& o)const
  {
    return C1097Int(((long long)m_iData + o.m_iData) % MOD);
  }
  C1097Int& operator+=(const C1097Int& o)
  {
    m_iData = ((long long)m_iData + o.m_iData) % MOD;
    return *this;
  }
  C1097Int& operator-=(const C1097Int& o)
  {
    m_iData = (m_iData + MOD - o.m_iData) % MOD;
    return *this;
  }
  C1097Int  operator-(const C1097Int& o)
  {
    return C1097Int((m_iData + MOD - o.m_iData) % MOD);
  }
  C1097Int  operator*(const C1097Int& o)const
  {
    return((long long)m_iData * o.m_iData) % MOD;
  }
  C1097Int& operator*=(const C1097Int& o)
  {
    m_iData = ((long long)m_iData * o.m_iData) % MOD;
    return *this;
  }
  bool operator<(const C1097Int& o)const
  {
    return m_iData < o.m_iData;
  }
  C1097Int pow(long long n)const
  {
    C1097Int iRet = 1, iCur = *this;
    while (n)
    {
      if (n & 1)
      {
        iRet *= iCur;
      }
      iCur *= iCur;
      n >>= 1;
    }
    return iRet;
  }
  C1097Int PowNegative1()const
  {
    return pow(MOD - 2);
  }
  int ToInt()const
  {
    return m_iData;
  }
private:
  int m_iData = 0;;
};
template<class ELE, class ResultType, ELE minEle, ELE maxEle>
class CLowUperr
{
public:
  CLowUperr(int iResutlCount) :m_iResutlCount(iResutlCount)
  {
  }
  void Init(const ELE* pLower, const ELE* pHigh, int iNum)
  {
    m_vPre.assign(4, vector<ResultType>(m_iResutlCount));
    if (iNum <= 0)
    {
      return;
    }
    InitPre(pLower, pHigh);
    iNum--;
    while (iNum--)
    {
      pLower++;
      pHigh++;
      vector<vector<ResultType>> dp(4, vector<ResultType>(m_iResutlCount));
      OnInitDP(dp);
      //处理非边界
      for (auto tmp = minEle; tmp <= maxEle; tmp++)
      {
        OnEnumOtherBit(dp[0], m_vPre[0], tmp);
      }
      //处理下边界
      OnEnumOtherBit(dp[1], m_vPre[1], *pLower);
      for (auto tmp = *pLower + 1; tmp <= maxEle; tmp++)
      {
        OnEnumOtherBit(dp[0], m_vPre[1], tmp);
      }
      //处理上边界
      OnEnumOtherBit(dp[2], m_vPre[2], *pHigh);
      for (auto tmp = minEle; tmp < *pHigh; tmp++)
      {
        OnEnumOtherBit(dp[0], m_vPre[2], tmp);
      }
      //处理上下边界
      if (*pLower == *pHigh)
      {
        OnEnumOtherBit(dp[3], m_vPre[3], *pLower);
      }
      else
      {
        OnEnumOtherBit(dp[1], m_vPre[3], *pLower);
        for (auto tmp = *pLower + 1; tmp < *pHigh; tmp++)
        {
          OnEnumOtherBit(dp[0], m_vPre[3], tmp);
        }
        OnEnumOtherBit(dp[2], m_vPre[3], *pHigh);
      }
      m_vPre.swap(dp);
    }
  }
  /*ResultType Total(int iMinIndex, int iMaxIndex)
  {
    ResultType ret;
    for (int status = 0; status < 4; status++)
    {
      for (int index = iMinIndex; index <= iMaxIndex; index++)
      {
        ret += m_vPre[status][index];
      }
    }
    return ret;
  }*/
protected:
  const int m_iResutlCount;
  void InitPre(const ELE* const pLower, const ELE* const pHigh)
  {
    for (ELE cur = *pLower; cur <= *pHigh; cur++)
    {
      int iStatus = 0;
      if (*pLower == cur)
      {
        iStatus = *pLower == *pHigh ? 3 : 1;
      }
      else if (*pHigh == cur)
      {
        iStatus = 2;
      }
      OnEnumFirstBit(m_vPre[iStatus], cur);
    }
  }
  virtual void OnEnumOtherBit(vector<ResultType>& dp, const vector<ResultType>& vPre, ELE curValue) = 0;
  virtual void OnEnumFirstBit(vector<ResultType>& vPre, const ELE curValue) = 0;
  virtual void OnInitDP(vector<vector<ResultType>>& dp)
  {
  }
  vector<vector<ResultType>> m_vPre;
};
class CCharLowerUper : public CLowUperr<char, C1097Int<>, 'a', 'z'>
{
public:
  CCharLowerUper(string evil):CLowUperr(evil.length())
  {
    m_evil = evil;
    m_vNext = KMP::Next(evil);
  }
  C1097Int<> Total()
  {
    return Total(0, m_iResutlCount - 1);
  }
  C1097Int<> Total(int iMinIndex, int iMaxIndex)
  {
    C1097Int<> ret = 0;
    for (int index = iMinIndex; index <= iMaxIndex; index++)
    {
      C1097Int<> cur = 0;
      for (int status = 0; status < 4; status++)
      {
        cur += m_vPre[status][index];
      }
      ret += cur;
    }
    return ret;
  }
protected:
  virtual void OnEnumFirstBit(vector< C1097Int<>>& vPre, const char curValue)
  {   
    const int mask = curValue == m_evil.front();
    if (mask < m_iResutlCount)
    {
      vPre[mask] += C1097Int<>(1);
    }
  }
  virtual void OnEnumOtherBit(vector< C1097Int<>>& dp, const vector< C1097Int<>>& vPre, char curValue)
  {
    for (int i = 0; i < m_iResutlCount; i++)
    {
      int next = i - 1;
      for (; (-1 != next) && (m_evil[next + 1] != curValue); next = m_vNext[next]);
      const int iNewLen = next + 1 + (m_evil[next + 1] == curValue);
      if (iNewLen < m_iResutlCount)
      {
        dp[iNewLen] += vPre[i];
      }
    }   
  }
  string m_evil;
  vector<int> m_vNext;
};
class Solution {
public:
  int findGoodStrings(int n, string s1, string s2, string evil) {
    C1097Int<> biRet = 0;
    const int len1 = s1.length();
    const int len2 = s2.length();
    if (len1 == len2)
    {
      CCharLowerUper lu(evil);
      lu.Init(s1.c_str(),s2.c_str(), len1);
      return lu.Total().ToInt();
    }
    {
      CCharLowerUper lu(evil);
      lu.Init(s1.c_str(), string(len1, 'z').c_str(), len1);
      biRet += lu.Total();
    }
    for (int i = len1+1; i < len2; i++)
    {
      CCharLowerUper lu(evil);
      lu.Init(string(i, 'a').c_str(), string(i, 'z').c_str(), i);
      biRet += lu.Total();
    }
    CCharLowerUper lu(evil);
    lu.Init(string(len2, 'a').c_str(), s2.c_str(), len2);
    biRet += lu.Total();
    return biRet.ToInt();
  }
};

测试用例

template<class T>
void Assert(const T& t1, const T& t2)
{
  assert(t1 == t2);
}
template<class T>
void Assert(const vector<T>& v1, const vector<T>& v2)
{
  if (v1.size() != v2.size())
  {
    assert(false);
    return;
  }
  for (int i = 0; i < v1.size(); i++)
  {
    Assert(v1[i], v2[i]);
  }
}
int main()
{ 
  int n;
  string s1, s2,  evil;
  {
    Solution sln;
    n = 2, s1 = "aa", s2 = "da", evil = "b";
    auto res = sln.findGoodStrings(n, s1, s2, evil);
    Assert(51, res);
  }
  {
    Solution sln;
    n = 8, s1 = "leetcode", s2 = "leetgoes", evil = "leet";
    auto res = sln.findGoodStrings(n, s1, s2, evil);
    Assert(0, res);
  }
  {
    Solution sln;
    n = 2, s1 = "gx", s2 = "gz", evil = "x";
    auto res = sln.findGoodStrings(n, s1, s2, evil);
    Assert(2, res);
  }
  {
    Solution sln;
    n = 93, s1 = "kazxkmmctdgtrplfggliycskmbfzjkrsthahcrxaaylpdykqfyejwteexytvxgjrbviconioomfpznawsseisfcpfkuvx", 
      s2 = "lajtokckoizywvirjhccouuhjkkshdtzchzmiccujzpeqzcvfekdqjgrbkzrwfnfwhyvzrrrakiausbleeimmthaqqouh", evil = "kpvphwnkrtxuiuhb";
    auto res = sln.findGoodStrings(n, s1, s2, evil);
    Assert(982374807, res);
  }
}

2023年1月15

class C1097Int

{

public:

C1097Int(int iData = 0) :m_iData(iData)

{

}

C1097Int operator+(const C1097Int& o)const

{

return C1097Int((m_iData + o.m_iData) % s_iMod);

}

C1097Int& operator+=(const C1097Int& o)

{

m_iData = (m_iData + o.m_iData) % s_iMod;

return this;
}
C1097Int operator
(const C1097Int& o)const

{

return((long long)m_iData o.m_iData) % s_iMod;
}
C1097Int& operator
=(const C1097Int& o)

{

m_iData =((long long)m_iData *o.m_iData) % s_iMod;

return *this;

}

int ToInt()const

{

return m_iData;

}

private:

int m_iData = 0;;

static const int s_iMod = 1000000007;

};

int operator+(int iData, const C1097Int& int1097)

{

int iRet = int1097.operator+(C1097Int(iData)).ToInt();

return iRet;

}

int& operator+=(int& iData, const C1097Int& int1097)

{

iData = int1097.operator+(C1097Int(iData)).ToInt();

return iData;

}

template

void MinSelf(T* seft, const T& other)

{

*seft = min(*seft, other);

}

template

void MaxSelf(T* seft, const T& other)

{

*seft = max(*seft, other);

}

int GetNotRepeateNum(int len, int iHasSel)

{

if (0 == len)

{

return 1;

}

if ((0 == iHasSel) && (1 == len))

{

return 10;

}

int iRet = 1;

if (iHasSel > 0)

{

for (int tmp = 10 - iHasSel; (tmp >= 2)&& len ; tmp–,len–)

{

iRet *= tmp;

}

}

else

{

iRet *= 9;

len–;

for (int tmp=9; (tmp>=2)&&len; len–,tmp–)

{

iRet *= tmp;

}

}

return iRet;

}

class Solution {

public:

int findGoodStrings(int n, string s1, string s2, string evil) {

//next[j]表示evil 前j+1个字符,最长相等前后缀,如果某个字符串的尾部j+1个字符和evil的前 j+1 个字符相等,则…尾部next[j]和…next[j]个字符相等

vector next(evil.length(),-1);

for (int i = 1, j = -1; i < next.size(); i++)

{

while ((j>=0) && (evil[i] != evil[j+1]))

{

j = next[j];

}

if (evil[i] == evil[j+1 ])

{

j++;

}

next[i] = j;

}

vector<vector> pre;

pre.assign(4, vector(evil.length() + 1));

pre[3][0] = 1;

for (int i = 0; i < s1.length(); i++ )

{

vector<vector> dp(4, vector(evil.length() + 1));

const char& charLow = s1[i];

const char& charUp = s2[i];

const bool bEqualRange = charLow == charUp;

for (int j = 0; j < evil.length(); j++)

{

for (char chCur = ‘a’; chCur <= ‘z’; chCur++)

{

int iNewEndLen = j;

while (iNewEndLen && (evil[iNewEndLen ] != chCur))

{

iNewEndLen = next[iNewEndLen-1]+1;

}

if (evil[iNewEndLen] == chCur)

{

iNewEndLen++;

}

dp[0][iNewEndLen] += pre[0][j];

//前一个字符 卡下限

if (chCur > charLow)

{

dp[0][iNewEndLen] += pre[1][j];

}

else if (charLow == chCur)

{

dp[1][iNewEndLen] += pre[1][j];

}

//前一个字符 卡上限

if (chCur < charUp)

{

dp[0][iNewEndLen] += pre[2][j];

}

else if (charUp == chCur)

{

dp[2][iNewEndLen] += pre[2][j];

}

//前一个字符串卡上下限

if ((charUp > chCur) && (charLow < chCur))

{

dp[0][iNewEndLen] += pre[3][j];

}

else if (bEqualRange)

{

if (charUp == chCur)

{

dp[3][iNewEndLen] += pre[3][j];

}

}

else

{

if (charUp == chCur)

{

dp[2][iNewEndLen] += pre[3][j];

}

if (charLow == chCur)

{

dp[1][iNewEndLen] += pre[3][j];

}

}

}

}

pre.swap(dp);

}

C1097Int sum;

for (int i = 0; i < 4; i++)

{

sum += std::accumulate(pre[i].begin(), pre[i].end() - 1, C1097Int());

}

return sum.ToInt();

}

};

2023年1月 第二版

class C1097Int

{

public:

C1097Int(int iData = 0) :m_iData(iData)

{

}
 C1097Int  operator+(const C1097Int& o)const
 {
   return C1097Int((m_iData + o.m_iData) % s_iMod);
 }
 C1097Int&  operator+=(const C1097Int& o)
 {
   m_iData = (m_iData + o.m_iData) % s_iMod;
   return *this;
 }
 C1097Int  operator*(const C1097Int& o)const
 {
   return((long long)m_iData *o.m_iData) % s_iMod;
 }
 C1097Int&  operator*=(const C1097Int& o)
 {
  m_iData =((long long)m_iData *o.m_iData) % s_iMod;
   return *this;
 }
 int ToInt()const
 {
   return m_iData;
 }

private:

int m_iData = 0;;

static const int s_iMod = 1000000007;

};

int operator+(int iData, const C1097Int& int1097)

{

int iRet = int1097.operator+(C1097Int(iData)).ToInt();

return iRet;

}

int& operator+=(int& iData, const C1097Int& int1097)

{

iData = int1097.operator+(C1097Int(iData)).ToInt();

return iData;

}

template

void MinSelf(T* seft, const T& other)

{

*seft = min(*seft, other);

}

template

void MaxSelf(T* seft, const T& other)

{

*seft = max(*seft, other);

}

int GetNotRepeateNum(int len, int iHasSel)

{

if (0 == len)

{

return 1;

}

if ((0 == iHasSel) && (1 == len))

{

return 10;

}

int iRet = 1;

if (iHasSel > 0)

{

for (int tmp = 10 - iHasSel; (tmp >= 2)&& len ; tmp–,len–)

{

iRet *= tmp;

}

}

else

{

iRet *= 9;

len–;

for (int tmp=9; (tmp>=2)&&len; len–,tmp–)

{

iRet *= tmp;

}

}

return iRet;

}

class Solution {

public:

int findGoodStrings(int n, string s1, string s2, string evil) {

//next[j]表示evil 前j+1个字符,最长相等前后缀,前后缀不能是本身

//如果某个字符串的尾部j+1个字符和evil的前 j+1 个字符相等,则…尾部next[j]和…next[j]个字符相等

vector next(evil.length());

for (int i = 1, j = 0; i < next.size(); i++)

{

while ( j && (evil[i] != evil[j]))

{

j = next[j-1];

}

if (evil[i] == evil[j])

{

j++;

}

next[i] = j;

}

vector<vector> pre;

pre.assign(4, vector(evil.length() + 1));

pre[3][0] = 1;

for (int i = 0; i < s1.length(); i++ )

{

vector<vector> dp(4, vector(evil.length() + 1));

const char& charLow = s1[i];

const char& charUp = s2[i];

const bool bEqualRange = charLow == charUp;

for (int j = 0; j < evil.length(); j++)

{

for (char chCur = ‘a’; chCur <= ‘z’; chCur++)

{

int iNewEndLen = j;

while (iNewEndLen && (evil[iNewEndLen ] != chCur))

{

iNewEndLen = next[iNewEndLen-1];

}

if (evil[iNewEndLen] == chCur)

{

iNewEndLen++;

}

dp[0][iNewEndLen] += pre[0][j];

//前一个字符 卡下限

if (chCur > charLow)

{

dp[0][iNewEndLen] += pre[1][j];

}

else if (charLow == chCur)

{

dp[1][iNewEndLen] += pre[1][j];

}

//前一个字符 卡上限

if (chCur < charUp)

{

dp[0][iNewEndLen] += pre[2][j];

}

else if (charUp == chCur)

{

dp[2][iNewEndLen] += pre[2][j];

}

//前一个字符串卡上下限

if ((charUp > chCur) && (charLow < chCur))

{

dp[0][iNewEndLen] += pre[3][j];

}

else if (bEqualRange)

{

if (charUp == chCur)

{

dp[3][iNewEndLen] += pre[3][j];

}

}

else

{

if (charUp == chCur)

{

dp[2][iNewEndLen] += pre[3][j];

}

if (charLow == chCur)

{

dp[1][iNewEndLen] += pre[3][j];

}

}

}

}

pre.swap(dp);

}

C1097Int sum;

for (int i = 0; i < 4; i++)

{

sum += std::accumulate(pre[i].begin(), pre[i].end() - 1, C1097Int());

}

return sum.ToInt();

}

};

2023年9月

using namespace std;

template

void OutToConsoleInner(const vector& vec, const string& strSep = " ")

{

for (int i = 0; i < vec.size(); i++)

{

if (0 != i % 25)

{

std::cout << strSep.c_str();

}

std::cout << setw(3) << setfill(’ ') << vec[i];

if (0 == (i + 1) % 25)

{

std::cout << std::endl;

}

else if (0 == (i + 1) % 5)

{

std::cout << strSep.c_str();

}

}

}

class CConsole

{

public:

template<class ELE>
static void Out(const vector<ELE>& vec, const string& strColSep = " ", const string& strRowSep = "\r\n")
{
  OutToConsoleInner(vec, strColSep);
  std::cout << strRowSep.c_str();
}
template<class ELE>
static void Out(const vector<vector<ELE>>& matrix, const string& strColSep = " ", const string& strRowSep = "\r\n")
{
  for (int i = 0; i < matrix.size(); i++)
  {
    OutToConsoleInner(matrix[i], strColSep);
    std::cout << strRowSep.c_str();
  }
}
template<class ELE>
static void Out(const std::map<ELE, std::vector<int> >& mTopPointToPoints, const string& strColSep = " ", const string& strRowSep = "\r\n")
{
  for (auto kv : mTopPointToPoints)
  {
    std::cout << kv.first << ":";
    OutToConsoleInner(kv.second, strColSep);
    std::cout << strRowSep.c_str();
  }
}
static void Out(const  std::string& t, const string& strColSep = " ", const string& strRowSep = "\r\n")
{
  std::cout << t.c_str() << strColSep.c_str();
}
template<class ELE  >
static void Out(const ELE& t, const string& strColSep = " ", const string& strRowSep = "\r\n")
{
  std::cout << t << strColSep.c_str();
}

};

void GenetateSum(vector& sums, const vector& nums)

{

sums.push_back(0);

for (int i = 0; i < nums.size(); i++)

{

sums.push_back(nums[i] + sums[i]);

}

}

//[iBegin,iEnd]之和

long long Total(int iBegin, int iEnd)

{

return (long long)(iBegin + iEnd) * (iEnd - iBegin + 1) / 2;

}

class CLadderhlp

{

public:

CLadderhlp(int ladders)

{

m_uLadderNum = ladders;

}

void AddNeedBick(int iNeedBick)

{

if (0 == m_uLadderNum)

{

return;

}

if (m_ladders.size() < m_uLadderNum)

{

m_ladders.push(iNeedBick);

m_iEaqualBicks += iNeedBick;

return;

}

int iTop = m_ladders.top();

if (iTop >= iNeedBick)

{

return;

}

m_iEaqualBicks -= iTop;

m_iEaqualBicks += iNeedBick;

m_ladders.pop();

m_ladders.push(iNeedBick);

}

std::priority_queue<int, vector, std::greater > m_ladders;

unsigned int m_uLadderNum;

long long m_iEaqualBicks = 0;

};

struct CPeo

{

CPeo(string strName, CPeo* pParent = nullptr)

{

m_strName = strName;

m_pParent = pParent;

}

string m_strName;

vector<CPeo*> m_childs;

CPeo* m_pParent = nullptr;

};

//通过 x &= (x-1)实现

int bitcount(unsigned x) {

int countx = 0;

while (x) {

countx++;

x &= (x - 1);

}

return countx;

}

int bitcount(unsigned long long x) {

int countx = 0;

while (x) {

countx++;

x &= (x - 1);

}

return countx;

}

class CRange

{

public:

template

CRange(const ELE& v)

{

m_iBegin = 0;

m_iEnd = v.size();

}

bool In(int iIndex)

{

return (iIndex >= m_iBegin) && (iIndex < m_iEnd);

}

const int End()

{

return m_iEnd;

}

protected:

int m_iBegin;

int m_iEnd;

};

template<class TData, TData defData,int iTypeNum = 26, char cBegin = ‘a’>

class CTrie

{

public:

CTrie()

{

}
template<class IT>
CTrie* Add(IT begin, IT end)
{
  CTrie* pNode = this;
  for (; begin != end; ++begin)
  {
    pNode = pNode->AddChar(*begin);
  }
  return pNode;
}
template<class IT>
CTrie* Search(IT begin, IT end)
{
  if (begin == end)
  {
    return this;
  }
  if ('.' == *begin)
  {
    for (auto& ptr : m_vPChilds)
    {
      if (!ptr)
      {
        continue;
      }
      auto pSearch = ptr->Search(begin + 1, end);
      if (pSearch)
      {
        return pSearch;
      }
    }
    return nullptr;
  }
  auto ptr = GetChild(*begin);
  if (nullptr == ptr)
  {
    return nullptr;
  }
  return ptr->Search(begin + 1, end);
}
TData m_data = defData;
CTrie* AddChar(char ch)
{
  if ((ch < cBegin) || (ch >= cBegin + iTypeNum))
  {
    return nullptr;
  }
  const int index = ch - cBegin;
  auto ptr = m_vPChilds[index];
  if (!ptr)
  {
    m_vPChilds[index] = new CTrie();
  }
  return m_vPChilds[index];
}
CTrie* GetChild(char ch)const
{
  if ((ch < cBegin) || (ch >= cBegin + iTypeNum))
  {
    return nullptr;
  }
  return m_vPChilds[ch - cBegin];
}

protected:

CTrie* m_vPChilds[iTypeNum] = { nullptr };

};

class CWords

{

public:

void Add(const string& word)

{

m_strStrs.insert(word);

}

bool Search(const string& word)

{

return Search(m_strStrs.begin(), m_strStrs.end(), 0, word.length(), word);

}

protected:

bool Search(std::set::const_iterator begin, std::set::const_iterator end, int iStrBegin, int iStrEnd, const string& str)

{

int i = iStrBegin;

for (; (i < iStrEnd) && (str[i] != ‘.’); i++);

auto it = std::equal_range(begin, end, str, [&iStrBegin, &i](const string& s, const string& sFind)

{

return s.substr(iStrBegin, i - iStrBegin) < sFind.substr(iStrBegin, i - iStrBegin);

});

if (i == iStrBegin)

{

it.first = begin;

it.second = end;

}

if (it.first == it.second)

{

return false;

}

if (i == iStrEnd)

{

return true;

}

if (i + 1 == iStrEnd)

{

return true;

}

string tmp = str;

for (char ch = ‘a’; ch <= ‘z’; ch++)

{

tmp[i] = ch;

auto ij = std::equal_range(it.first, it.second, tmp, [&ch, &i](const string& s, const string& sFind)

{

return s[i] < sFind[i];

});

if (ij.first == ij.second)

{

continue;

}

if (Search(ij.first, ij.second, i + 1, iStrEnd, str))
    {
      return true;
    }
  }
  return false;
}
std::set<string> m_strStrs;

};

class WordDictionary {

public:

WordDictionary() {

for (int i = 0; i < 26; i++)

{

m_str[i] = std::make_unique();

}

}

void addWord(string word) {
  m_str[word.length()]->Add(word);
}
bool search(string word) {
  return m_str[word.length()]->Search(word);
}
std::unique_ptr<CWords> m_str[26];

};

template

class C1097Int

{

public:

C1097Int(long long llData = 0) :m_iData(llData% MOD)

{

}
C1097Int  operator+(const C1097Int& o)const
{
  return C1097Int(((long long)m_iData + o.m_iData) % MOD);
}
C1097Int& operator+=(const C1097Int& o)
{
  m_iData = ((long long)m_iData + o.m_iData) % MOD;
  return *this;
}
C1097Int& operator-=(const C1097Int& o)
{
  m_iData = (m_iData + MOD - o.m_iData) % MOD;
  return *this;
}
C1097Int  operator-(const C1097Int& o)
{
  return C1097Int((m_iData + MOD - o.m_iData) % MOD);
}
C1097Int  operator*(const C1097Int& o)const
{
  return((long long)m_iData * o.m_iData) % MOD;
}
C1097Int& operator*=(const C1097Int& o)
{
  m_iData = ((long long)m_iData * o.m_iData) % MOD;
  return *this;
}
bool operator<(const C1097Int& o)const
{
  return m_iData < o.m_iData;
}
C1097Int pow(int n)const
{
  C1097Int iRet = 1, iCur = *this;
  while (n)
  {
    if (n & 1)
    {
      iRet *= iCur;
    }
    iCur *= iCur;
    n >>= 1;
  }
  return iRet;
}
C1097Int PowNegative1()const
{
  return pow(MOD - 2);
}
int ToInt()const
{
  return m_iData;
}

private:

int m_iData = 0;;

};

template

int operator+(int iData, const C1097Int& int1097)

{

int iRet = int1097.operator+(C1097Int(iData)).ToInt();

return iRet;

}

template

int& operator+=(int& iData, const C1097Int& int1097)

{

iData = int1097.operator+(C1097Int(iData)).ToInt();

return iData;

}

template

int operator*(int iData, const C1097Int& int1097)

{

int iRet = int1097.operator*(C1097Int(iData)).ToInt();

return iRet;

}

template

int& operator*=(int& iData, const C1097Int& int1097)

{

iData = int1097.operator*(C1097Int(iData)).ToInt();

return iData;

}

template

void MinSelf(ELE* seft, const ELE& other)

{

*seft = min(*seft, other);

}

template

void MaxSelf(ELE* seft, const ELE& other)

{

*seft = max(*seft, other);

}

int GetNotRepeateNum(int len, int iHasSel)

{

if (0 == len)

{

return 1;

}

if ((0 == iHasSel) && (1 == len))

{

return 10;

}

int iRet = 1;

if (iHasSel > 0)

{

for (int tmp = 10 - iHasSel; (tmp >= 2) && len; tmp–, len–)

{

iRet *= tmp;

}

}

else

{

iRet *= 9;

len–;

for (int tmp = 9; (tmp >= 2) && len; len–, tmp–)

{

iRet *= tmp;

}

}

return iRet;

}

int GCD(int n1, int n2)

{

int t1 = min(n1, n2);

int t2 = max(n1, n2);

if (0 == t1)

{

return t2;

}

return GCD(t2 % t1, t1);

}

void CreateMaskVector(vector& v, const int* const p, int n)

{

const int iMaxMaskNum = 1 << n;

v.resize(iMaxMaskNum);

for (int i = 0; i < n; i++)

{

v[1 << i] = p[i];

}

for (int mask = 1; mask < iMaxMaskNum; mask++)

{

const int iSubMask = mask & (-mask);

v[mask] = v[iSubMask] + v[mask - iSubMask];

}

}

class CMaxLineTree

{

public:

CMaxLineTree(int iArrSize) :m_iArrSize(iArrSize), m_vData(iArrSize * 4)

{

}
//iIndex 从0开始
void Modify(int iIndex, int iValue)
{
  Modify(1, 1, m_iArrSize, iIndex + 1, iValue);
}
//iNeedQueryLeft iNeedQueryRight 从0开始
int Query(const int iNeedQueryLeft, const int iNeedQueryRight)
{
  return Query(1, 1, m_iArrSize, iNeedQueryLeft + 1, iNeedQueryRight + 1);
}
//返回第一个大于等于iMax的节点索引,没有大于等于iMax,则返回-1
int GetFirstMaxIndex(int iMax)
{
  int iNO = 1;
  if (m_vData[1] < iMax)
  {
    return -1;
  }
  int left = 1, r = m_iArrSize;
  while (r > left)
  {
    const int mid = (left + r) / 2;
    if (m_vData[iNO * 2] < iMax)
    {
      iNO = iNO * 2 + 1;
      left = mid + 1;
    }
    else
    {
      iNO *= 2;
      r = mid;
    }
  }
  return r - 1;
}

protected:

int Query(const int iTreeNodeIndex, const int iRecordLeft, const int iRecordRight, const int iNeedQueryLeft, const int iNeedQueryRight)

{

if ((iNeedQueryLeft <= iRecordLeft) && (iNeedQueryRight >= iRecordRight))

{

return m_vData[iTreeNodeIndex];

}

const int iMid = (iRecordLeft + iRecordRight) / 2;

int iRet = 0;

if (iNeedQueryLeft <= iMid)

{

iRet = Query(iTreeNodeIndex * 2, iRecordLeft, iMid, iNeedQueryLeft, iNeedQueryRight);

}

if (iNeedQueryRight > iMid)

{

iRet = max(iRet, Query(iTreeNodeIndex * 2 + 1, iMid + 1, iRecordRight, iNeedQueryLeft, iNeedQueryRight));

}

return iRet;

}

void Modify(int iTreeNodeIndex, int iLeft, int iRight, int iIndex, int iValue)

{

if (iLeft == iRight)

{

m_vData[iTreeNodeIndex] = iValue;

return;

}

const int iMid = (iLeft + iRight) / 2;

if (iIndex <= iMid)

{

Modify(iTreeNodeIndex * 2, iLeft, iMid, iIndex, iValue);

}

else

{

Modify(iTreeNodeIndex * 2 + 1, iMid + 1, iRight, iIndex, iValue);

}

m_vData[iTreeNodeIndex] = max(m_vData[iTreeNodeIndex * 2], m_vData[iTreeNodeIndex * 2 + 1]);

}

const int m_iArrSize;

std::vector m_vData;

};

class CMaxLineTreeMap

{

public:

CMaxLineTreeMap(int iArrSize) :m_iArrSize(iArrSize)

{

}
//iIndex 从0开始
void Modify(int iIndex, int iValue)
{
  Modify(1, 1, m_iArrSize, iIndex + 1, iValue);
}
//iNeedQueryLeft iNeedQueryRight 从0开始
int Query(const int iNeedQueryLeft, const int iNeedQueryRight)
{
  return Query(1, 1, m_iArrSize, iNeedQueryLeft + 1, iNeedQueryRight + 1);
}

protected:

int Query(const int iTreeNodeIndex, const int iRecordLeft, const int iRecordRight, const int iNeedQueryLeft, const int iNeedQueryRight)

{

if ((iNeedQueryLeft <= iRecordLeft) && (iNeedQueryRight >= iRecordRight))

{

return m_mData[iTreeNodeIndex];

}

const int iMid = (iRecordLeft + iRecordRight) / 2;

int iRet = 0;

if (iNeedQueryLeft <= iMid)

{

iRet = Query(iTreeNodeIndex * 2, iRecordLeft, iMid, iNeedQueryLeft, iNeedQueryRight);

}

if (iNeedQueryRight > iMid)

{

iRet = max(iRet, Query(iTreeNodeIndex * 2 + 1, iMid + 1, iRecordRight, iNeedQueryLeft, iNeedQueryRight));

}

return iRet;

}

void Modify(int iTreeNodeIndex, int iLeft, int iRight, int iIndex, int iValue)

{

if (iLeft == iRight)

{

m_mData[iTreeNodeIndex] = iValue;

return;

}

const int iMid = (iLeft + iRight) / 2;

if (iIndex <= iMid)

{

Modify(iTreeNodeIndex * 2, iLeft, iMid, iIndex, iValue);

}

else

{

Modify(iTreeNodeIndex * 2 + 1, iMid + 1, iRight, iIndex, iValue);

}

m_mData[iTreeNodeIndex] = max(m_mData[iTreeNodeIndex * 2], m_mData[iTreeNodeIndex * 2 + 1]);

}

const int m_iArrSize;

std::unordered_map<int, int> m_mData;

};

template

class CSumLineTree

{

public:

CSumLineTree(int iEleSize) :m_iEleSize(iEleSize), m_vArr(m_iEleSize * 4), m_vChildAdd(m_iEleSize * 4)

{

}
void Add(int iLeftIndex, int iRightIndex, int iValue)
{
  Add(1, 1, m_iEleSize, iLeftIndex + 1, iRightIndex + 1, iValue);
}
ELE Query(int iLeftIndex, int iRightIndex)
{
  return Query(1, 1, m_iEleSize, iLeftIndex + 1, iRightIndex + 1);
}

private:

ELE Query(int iNode, int iDataLeft, int iDataRight, int iOpeLeft, int iOpeRight)

{

if ((iOpeLeft <= iDataLeft) && (iOpeRight >= iDataRight))

{

return m_vArr[iNode];

}

Fresh(iNode, iDataLeft, iDataRight);

const int iMid = iDataLeft + (iDataRight - iDataLeft) / 2;

ELE ret(0);

if (iMid >= iOpeLeft)

{

ret += Query(iNode * 2, iDataLeft, iMid, iOpeLeft, iOpeRight);

}

if (iMid + 1 <= iOpeRight)

{

ret += Query(iNode * 2 + 1, iMid + 1, iDataRight, iOpeLeft, iOpeRight);

}

return ret;

}

/* 暴力解法

void Add(int iNode, int iDataLeft, int iDataRight, int iOpeLeft, int iOpeRight, int iValue)

{

m_vArr[iNode] += T(iValue)*(min(iDataRight, iOpeRight) - max(iDataLeft, iOpeLeft)+1);

if (iDataLeft == iDataRight)

{

return;

}

const int iMid = iDataLeft + (iDataRight - iDataLeft) / 2;

if (iMid >= iOpeLeft)

{

Add(iNode * 2, iDataLeft, iMid, iOpeLeft, iOpeRight, iValue);

}

if (iMid + 1 <= iOpeRight)

{

Add(iNode * 2 + 1, iMid + 1, iDataRight, iOpeLeft, iOpeRight, iValue);

}

}

*/

void Fresh(int iNode, int iDataLeft, int iDataRight)

{

const int iMid = iDataLeft + (iDataRight - iDataLeft) / 2;

if (m_vChildAdd[iNode] != 0)

{

Add(iNode * 2, iDataLeft, iMid, iDataLeft, iMid, m_vChildAdd[iNode]);

Add(iNode * 2 + 1, iMid + 1, iDataRight, iMid + 1, iDataRight, m_vChildAdd[iNode]);

m_vChildAdd[iNode] = 0;

}

}

//懒惰法

void Add(int iNode, int iDataLeft, int iDataRight, int iOpeLeft, int iOpeRight, int iValue)

{

m_vArr[iNode] += ELE(iValue) * (min(iDataRight, iOpeRight) - max(iDataLeft, iOpeLeft) + 1);

if ((iOpeLeft <= iDataLeft) && (iOpeRight >= iDataRight))

{

m_vChildAdd[iNode] += ELE(iValue);

return;

}

Fresh(iNode, iDataLeft, iDataRight);
  const int iMid = iDataLeft + (iDataRight - iDataLeft) / 2;
  if (iMid >= iOpeLeft)
  {
    Add(iNode * 2, iDataLeft, iMid, iOpeLeft, iOpeRight, iValue);
  }
  if (iMid + 1 <= iOpeRight)
  {
    Add(iNode * 2 + 1, iMid + 1, iDataRight, iOpeLeft, iOpeRight, iValue);
  }
}
const int m_iEleSize;
vector<ELE> m_vArr;
vector<int> m_vChildAdd;

};

template

class CTreeArr

{

public:

CTreeArr(int iSize) :m_vData(iSize + 1)

{

}
void Add(int index, ELE value)
{
  index++;
  while (index < m_vData.size())
  {
    m_vData[index] += value;
    index += index & (-index);
  }
}
ELE Sum(int index)
{
  index++;
  ELE ret = 0;
  while (index)
  {
    ret += m_vData[index];
    index -= index & (-index);
  }
  return ret;
}
ELE Get(int index)
{
  return Sum(index) - Sum(index - 1);
}

private:

vector m_vData;

};

//iCodeNum 必须大于等于可能的字符数

template

class CHashStr {

public:

CHashStr(string s, int iCodeNum, int iCodeBegin = 1, char chBegin = ‘a’) {

m_c = s.length();

m_vP.resize(m_c + 1);

m_vP[0] = 1;

m_vHash.resize(m_c + 1);

for (int i = 0; i < m_c; i++)

{

const int P = iCodeBegin + iCodeNum;

m_vHash[i + 1] = m_vHash[i] * P + s[i] - chBegin + iCodeBegin;

m_vP[i + 1] = m_vP[i] * P;

}

}

//iMinValue将被编码为0,iMaxValue被编码为iMaxValue-iMinValue。

CHashStr(const int* data,int len, int iMinValue = 0, int iMaxValue = 9 ) {

m_c = len;

m_vP.resize(m_c + 1);

m_vP[0] = 1;

m_vHash.resize(m_c + 1);

const int P = iMaxValue - iMinValue + 1;

for (int i = 0; i < m_c; i++)

{

const int iCurCode = data[i] - iMinValue;

assert((iCurCode >= 0) && (iCurCode < P));

m_vHash[i + 1] = m_vHash[i] * P + iCurCode;

m_vP[i + 1] = m_vP[i] * P;

}

}

//包括left right

int GetHash(int left, int right)

{

return (m_vHash[right + 1] - m_vHash[left] * m_vP[right - left + 1]).ToInt();

}

inline int GetHash(int right)

{

return m_vHash[right + 1].ToInt();

}

int GetHashExincludeRight(int left, int right)

{

return (m_vHash[right ] - m_vHash[left] * m_vP[right - left ]).ToInt();

}

inline int GetHashExincludeRight(int right)

{

return m_vHash[right].ToInt();

}

int m_c;

vector<C1097Int> m_vP;

vector<C1097Int> m_vHash;

};

template

class C2HashStr

{

public:

C2HashStr(string s) {

m_pHash1 = std::make_unique<CHashStr<>>(s, 26);

m_pHash2 = std::make_unique < CHashStr>(s, 27, 0);

}

C2HashStr(const int* data, int len, int iMinValue = 0, int iMaxValue = 9)

{

m_pHash1 = std::make_unique<CHashStr<>>(data, len, iMinValue, iMaxValue);

m_pHash2 = std::make_unique < CHashStr>(data, len, iMinValue, iMaxValue);

}

//包括left right

long long GetHash(int left, int right)

{

return (long long)m_pHash1->GetHash(left, right) * (MOD2 + 1) + m_pHash2->GetHash(left, right);

}

long long GetHash(int right)

{

return (long long)m_pHash1->GetHash(right) * (MOD2 + 1) + m_pHash2->GetHash(right);

}

//包括Left,不包括Right

long long GetHashExincludeRight(int left, int right)

{

return (long long)m_pHash1->GetHashExincludeRight(left, right) * (MOD2 + 1) + m_pHash2->GetHashExincludeRight(left, right);

}

long long GetHashExincludeRight(int right)

{

return (long long)m_pHash1->GetHashExincludeRight(right) * (MOD2 + 1) + m_pHash2->GetHashExincludeRight(right);

}

private:

std::unique_ptr<CHashStr<>> m_pHash1;

std::unique_ptr<CHashStr> m_pHash2;

};

template

class CDynaHashStr {

public:

CDynaHashStr(int iCodeNum, int iCodeBegin = 1, char chBegin = ‘a’) :m_iUnit(iCodeNum + iCodeBegin), m_iP(1), m_iBegin(iCodeBegin - chBegin)

{

}
inline void push_back(const char& ch)
{
  const int iNum = ch + m_iBegin;
  m_iHash *= m_iUnit;
  m_iHash += iNum;
  m_iP *= m_iUnit;
}
inline void push_front(const char& ch)
{
  const int iNum = ch + m_iBegin;
  m_iHash += m_iP * iNum;
  m_iP *= m_iUnit;
}
inline int GetHash() const
{
  return m_iHash;
}
const int m_iUnit;
const int m_iBegin;
C1097Int<MOD> m_iHash;
C1097Int<MOD> m_iP;

};

template

class C2DynaHashStr {

public:

C2DynaHashStr(int iCodeNum, int iCodeBegin = 1, char chBegin = ‘a’)

{

m_pHash1 = new CDynaHashStr<>(iCodeNum, iCodeBegin, chBegin);

m_pHash2 = new CDynaHashStr(iCodeNum, iCodeBegin, chBegin);

}

~C2DynaHashStr()

{

delete m_pHash1;

delete m_pHash2;

}

inline void push_back(const char& ch)

{

m_pHash1->push_back(ch);

m_pHash2->push_back(ch);

}

inline void push_front(const char& ch)

{

m_pHash1->push_front(ch);

m_pHash2->push_front(ch);

}

long long Hash()const

{

return (long long)MOD2 * m_pHash1->m_iHash.ToInt() + m_pHash2->m_iHash.ToInt();

}

bool operator==(const C2DynaHashStr& other) const

{

return (m_pHash1->m_iHash.ToInt() == other.m_pHash1->m_iHash.ToInt()) && (m_pHash2->m_iHash.ToInt() == other.m_pHash2->m_iHash.ToInt());

}

CDynaHashStr<>* m_pHash1;

CDynaHashStr* m_pHash2;

};

namespace NSort

{

template

bool SortVecVec(const vector& v1, const vector& v2)

{

return v1[ArrIndex] < v2[ArrIndex];

};

template<class T >
void ShellSort(vector<T>& v)
{
  T tMax = *std::max_element(v.begin(), v.end());
  T exp = 1;
  while (tMax >= exp)
  {
    int vNums[10] = { 0 };
    for (const auto& n : v)
    {
      vNums[n / exp % 10]++;
    }
    int indexs[10] = { 0 };
    for (int i = 1; i < 10; i++)
    {
      indexs[i] = vNums[i - 1] + indexs[i-1];
    }
    vector<T> tmp(v.size());
    for (const auto& n : v)
    {
      const int cur = n / exp % 10;
      tmp[indexs[cur]] = n;
      indexs[cur]++;
    }
    v.swap(tmp);
    exp *= 10;
  }
}
template<class T,class _Pr = less<T> >
void MergeSort(vector<T>& v, const vector<T>& v1, const vector<T>& v2)
{
  int i1 = 0, i2 = 0;
  while ((i1 < v1.size()) && (i2 < v2.size()))
  {
    if (std::less()(v1[i1], v2[i2]))
    {
      v.emplace_back(v1[i1++]);
    }
    else
    {
      v.emplace_back(v2[i2++]);
    }
  }
  while (i1 < v1.size())
  {
    v.emplace_back(v1[i1++]);
  }
  while (i2 < v2.size())
  {
    v.emplace_back(v2[i2++]);
  }
}

}

namespace NCmp

{

template

bool Less(const std::pair<Class1, int>& p, Class1 iData)

{

return p.first < iData;

}

template<class Class1>
bool  Greater(const std::pair<Class1, int>& p, Class1 iData)
{
  return p.first > iData;
}
template<class _Ty1, class _Ty2>
class CLessPair
{
public:
  bool operator()(const std::pair<_Ty1, _Ty2>& p1, const std::pair<_Ty1, _Ty2>& p2)const
  {
    return p1.first < p2.first;
  }
};
template<class _Ty1, class _Ty2>
class CGreatePair
{
public:
  bool operator()(const std::pair<_Ty1, _Ty2>& p1, const std::pair<_Ty1, _Ty2>& p2)const
  {
    return p1.first > p2.first;
  }
};

}

class CIndexVector

{

public:

template

CIndexVector(vector& data)

{

for (int i = 0; i < data.size(); i++)

{

m_indexs.emplace_back(i);

}

std::sort(m_indexs.begin(), m_indexs.end(), [data](const int& i1, const int& i2)

{

return data[i1] < data[i2];

});

}

int GetIndex(int index)

{

return m_indexs[index];

}

private:

vector m_indexs;

};

class CMedian

{

public:

void AddNum(int iNum)

{

m_queTopMin.emplace(iNum);

MakeNumValid();

MakeSmallBig();

}

void Remove(int iNum)

{

if (m_queTopMax.size() && (iNum <= m_queTopMax.top()))

{

m_setTopMaxDel.insert(iNum);

}

else

{

m_setTopMinDel.insert(iNum);

}

PopIsTopIsDel(m_queTopMin, m_setTopMinDel);
  PopIsTopIsDel(m_queTopMax, m_setTopMaxDel);
  MakeNumValid();
  MakeSmallBig();
}
double Median()
{
  const int iMaxNum = m_queTopMin.size() - m_setTopMinDel.size();
  const int iMinNum = m_queTopMax.size() - m_setTopMaxDel.size();
  if (iMaxNum > iMinNum)
  {
    return m_queTopMin.top();
  }
  return ((double)m_queTopMin.top() + m_queTopMax.top()) / 2.0;
}
template<class ELE>
void PopIsTopIsDel(ELE& que, std::unordered_multiset<int>& setTopMaxDel)
{
  while (que.size() && (setTopMaxDel.count(que.top())))
  {
    setTopMaxDel.erase(setTopMaxDel.find(que.top()));
    que.pop();
  }
}
void MakeNumValid()
{
  const int iMaxNum = m_queTopMin.size() - m_setTopMinDel.size();
  const int iMinNum = m_queTopMax.size() - m_setTopMaxDel.size();
  //确保两个队的数量
  if (iMaxNum > iMinNum + 1)
  {
    int tmp = m_queTopMin.top();
    m_queTopMin.pop();
    m_queTopMax.emplace(tmp);
    PopIsTopIsDel(m_queTopMin, m_setTopMinDel);
  }
  if (iMinNum > iMaxNum)
  {
    int tmp = m_queTopMax.top();
    m_queTopMax.pop();
    m_queTopMin.push(tmp);
    PopIsTopIsDel(m_queTopMax, m_setTopMaxDel);
  }
}
void MakeSmallBig()
{
  if (m_queTopMin.empty() || m_queTopMax.empty())
  {
    return;
  }
  while (m_queTopMin.top() < m_queTopMax.top())
  {
    const int iOldTopMin = m_queTopMin.top();
    const int iOldTopMax = m_queTopMax.top();
    m_queTopMin.pop();
    m_queTopMax.pop();
    m_queTopMin.emplace(iOldTopMax);
    m_queTopMax.emplace(iOldTopMin);
    PopIsTopIsDel(m_queTopMin, m_setTopMinDel);
    PopIsTopIsDel(m_queTopMax, m_setTopMaxDel);
  }
}
std::priority_queue<int> m_queTopMax;
std::priority_queue<int, vector<int>, greater<int>> m_queTopMin;
std::unordered_multiset<int> m_setTopMaxDel, m_setTopMinDel;

};

template

class CDistanceGrid

{

public:

CDistanceGrid(const vector<vector>& grid) :m_grid(grid), m_r(grid.size()), m_c(grid[0].size())

{

}
//单源路径 D 算法 ,时间复杂度:r*c*log(r*c)
inline int Dis(int r1, int c1, int r2, int c2)
{
  vector<vector<int>> vDis(iMaxRow, vector<int>(iMaxCol, INT_MAX));
  auto Add = [&vDis, this](std::priority_queue<pair<int, int>, vector<std::pair<int, int>>, greater<pair<int, int>>>& queCur, int iDis, int r, int c)
  {
    const int iRowColMask = iMaxCol * r + c;
    if (iDis >= vDis[r][c])
    {
      return;
    }
    queCur.emplace(iDis, iRowColMask);
    vDis[r][c] = iDis;
  };
  auto Move = [&](std::priority_queue<pair<int, int>, vector<std::pair<int, int>>, greater<pair<int, int>>>& queCur, int iDis, int r, int c)
  {
    if ((r < 0) || (r >= m_r))
    {
      return;
    }
    if ((c < 0) || (c >= m_c))
    {
      return;
    }
    if (m_grid[r][c] < 1)
    {
      return;
    }
    Add(queCur, iDis, r, c);
  };
  std::priority_queue<pair<int, int>, vector<std::pair<int, int>>, greater<pair<int, int>>> que;
  Add(que, 0, r1, c1);
  while (que.size())
  {
    const int iDis = que.top().first;
    const int iStart = que.top().second;
    que.pop();
    const int r = iStart / iMaxCol;
    const int c = iStart % iMaxCol;
    if ((r == r2) && (c == c2))
    {
      return iDis;
    }
    if (iDis > vDis[r][c])
    {
      continue;
    }
    Move(que, iDis + 1, r + 1, c);
    Move(que, iDis + 1, r - 1, c);
    Move(que, iDis + 1, r, c + 1);
    Move(que, iDis + 1, r, c - 1);
  }
  return -1;
}

private:

virtual bool IsCanMoveStatue(int r, int c)

{

return m_grid[r][c] >= 1;

}

const int m_r;

const int m_c;

const vector<vector>& m_grid;

};

class CBFSGridDist

{

public:

CBFSGridDist(const vector<vector>& bCanVisit, int r, int c) :m_bCanVisit(bCanVisit), m_r(m_bCanVisit.size()), m_c(m_bCanVisit[0].size())

{

m_vDis.assign(m_r, vector(m_c, INT_MAX / 2));

Dist(r, c);

}

bool Vilid(const int r, const int c)

{

if ((r < 0) || (r >= m_r))

{

return false;

}

if ((c < 0) || (c >= m_c))

{

return false;

}

return true;

}

const vector<vector>& Dis()const

{

return m_vDis;

}

const vector<vector>& m_bCanVisit;

private:

//INT_MAX/2 表示无法到达

void Dist(int r, int c)

{

m_vDis.assign(m_r, vector(m_c, INT_MAX / 2));

vector<vector> vHasDo(m_r, vector(m_c));

std::queue<std::pair<int, int>> que;

auto Add = [&](const int& r, const int& c, const int& iDis)

{

if (!Vilid(r, c))

{

return;

}

if (vHasDo[r][c])

{

return;

}

if (!m_bCanVisit[r][c])

{

vHasDo[r][c] = true;

return;

}

if (iDis >= m_vDis[r][c])

{

return;

}

que.emplace(r, c);
    m_vDis[r][c] = iDis;
    vHasDo[r][c] = true;
  };
  Add(r, c, 0);
  while (que.size())
  {
    const int r = que.front().first;
    const int c = que.front().second;
    que.pop();
    const int iDis = m_vDis[r][c];
    Add(r + 1, c, iDis + 1);
    Add(r - 1, c, iDis + 1);
    Add(r, c + 1, iDis + 1);
    Add(r, c - 1, iDis + 1);
  }
}
vector<vector<int>> m_vDis;
const int m_r;
const int m_c;

};

class C2BNumTrieNode

{

public:

C2BNumTrieNode()

{

m_childs[0] = m_childs[1] = nullptr;

}

bool GetNot0Child(bool bFirstRight)

{

auto ptr = m_childs[bFirstRight];

if (ptr && (ptr->m_iNum > 0))

{

return bFirstRight;

}

return !bFirstRight;

}

int m_iNum = 0;

C2BNumTrieNode* m_childs[2];

};

template

class C2BNumTrie

{

public:

C2BNumTrie()

{

m_pRoot = new C2BNumTrieNode();

}

void Add(int iNum)

{

m_setHas.emplace(iNum);

C2BNumTrieNode* p = m_pRoot;

for (int i = iLeveNum - 1; i >= 0; i–)

{

p->m_iNum++;

bool bRight = iNum & (1 << i);

if (nullptr == p->m_childs[bRight])

{

p->m_childs[bRight] = new C2BNumTrieNode();

}

p = p->m_childs[bRight];

}

p->m_iNum++;

}

void Del(int iNum)

{

auto it = m_setHas.find(iNum);

if (m_setHas.end() == it)

{

return;

}

m_setHas.erase(it);

C2BNumTrieNode* p = m_pRoot;

for (int i = iLeveNum - 1; i >= 0; i–)

{

p->m_iNum–;

bool bRight = iNum & (1 << i);

p = p->m_childs[bRight];

}

p->m_iNum–;

}

int MaxXor(int iNum)

{

C2BNumTrieNode* p = m_pRoot;

int iRet = 0;

for (int i = iLeveNum - 1; i >= 0; i–)

{

bool bRight = !(iNum & (1 << i));

bool bSel = p->GetNot0Child(bRight);

p = p->m_childs[bSel];

if (bSel == bRight)

{

iRet |= (1 << i);

}

}

return iRet;

}

C2BNumTrieNode* m_pRoot;

std::unordered_multiset m_setHas;

};

struct SValueItem

{

SValueItem()

{

}
SValueItem(int iValue)
{
  m_iCoefficient = iValue;
}
SValueItem operator*(const SValueItem& o)const
{
  SValueItem ret(m_iCoefficient * o.m_iCoefficient);
  int i = 0, j = 0;
  while ((i < m_vVars.size()) && (j < o.m_vVars.size()))
  {
    if (m_vVars[i] < o.m_vVars[j])
    {
      ret.m_vVars.emplace_back(m_vVars[i]);
      i++;
    }
    else
    {
      ret.m_vVars.emplace_back(o.m_vVars[j]);
      j++;
    }
  }
  ret.m_vVars.insert(ret.m_vVars.end(), m_vVars.begin() + i, m_vVars.end());
  ret.m_vVars.insert(ret.m_vVars.end(), o.m_vVars.begin() + j, o.m_vVars.end());
  return ret;
}
bool operator<(const SValueItem& o)const
{
  if (m_vVars.size() == o.m_vVars.size())
  {
    return m_vVars < o.m_vVars;
  }
  return m_vVars.size() > o.m_vVars.size();
}
vector<std::string> m_vVars;
int m_iCoefficient = 1;//系数、倍率
std::string ToString()const
{
  std::ostringstream os;
  os << m_iCoefficient;
  for (const auto& s : m_vVars)
  {
    os << "*" << s;
  }
  return os.str();
}

};

struct SValue

{

SValue()

{

}
SValue(int iValue)
{
  SValueItem item;
  item.m_iCoefficient = iValue;
  m_items.emplace(item);
}
SValue(std::string strName)
{
  SValueItem item;
  item.m_vVars.emplace_back(strName);
  m_items.emplace(item);
}
SValue operator-(const SValue& o)const
{
  SValue ret;
  ret.m_items = m_items;
  for (auto it : o.m_items)
  {
    ret -= it;
  }
  return ret;
}
SValue operator+(const SValue& o)const
{
  SValue ret;
  ret.m_items = m_items;
  for (auto it : o.m_items)
  {
    ret += it;
  }
  return ret;
}
SValue operator*(const SValue& o)const
{
  SValue ret;
  for (const auto it : m_items)
  {
    for (const auto ij : o.m_items)
    {
      ret += it * ij;
    }
  }
  return ret;
}
SValue& operator+=(const SValueItem& item)
{
  auto it = m_items.find(item);
  if (m_items.end() == it)
  {
    m_items.emplace(item);
  }
  else
  {
    auto tmp = *it;
    tmp.m_iCoefficient += item.m_iCoefficient;
    m_items.erase(it);
    m_items.emplace(tmp);
  }
  return *this;
}
SValue& operator-=(const SValueItem& item)
{
  auto it = m_items.find(item);
  if (m_items.end() == it)
  {
    auto tmp = item;
    tmp.m_iCoefficient *= -1;
    m_items.emplace(tmp);
  }
  else
  {
    auto tmp = *it;
    tmp.m_iCoefficient -= item.m_iCoefficient;
    m_items.erase(it);
    m_items.emplace(tmp);
  }
  return *this;
}
vector<std::string> ToStrings()const
{
  vector<std::string> vRet;
  for (const auto& item : m_items)
  {
    if (0 == item.m_iCoefficient)
    {
      continue;
    }
    vRet.emplace_back(item.ToString());
  }
  return vRet;
}
std::set<SValueItem> m_items;

};

class CDelIndexs

{

public:

CDelIndexs()

{

}
CDelIndexs(int iSize)
{
  Init(iSize);
}
void Init(int iSize)
{
  m_bDels.assign(iSize, false);
  m_vNext.resize(iSize);
  for (int i = 0; i < iSize; i++)
  {
    m_vNext[i] = i + 1;
  }
}
void Del(int index)
{
  if ((index < 0) || (index >= m_vNext.size()))
  {
    return;
  }
  if (m_bDels[index])
  {
    return;
  }
  m_bDels[index] = true;
}
void SetCur(int index)
{
  if (index < 0)
  {
    m_iCur = m_vNext.size();
  }
  else
  {
    m_iCur = FreshCur(index);
  }
}
int NextIndex()
{
  if (m_iCur >= m_vNext.size())
  {
    return -1;
  }
  auto ret = m_iCur;
  SetCur(m_vNext[m_iCur]);
  return ret;
}

private:

int FreshCur(int index)

{

if (index >= m_vNext.size())

{

return m_vNext.size();

}

if (!m_bDels[index])

{

return index;

}

return m_vNext[index] = FreshCur(m_vNext[index]);
}
int m_iCur = 0;
vector<bool> m_bDels;
vector<int> m_vNext;

};

class CUnionFind

{

public:

CUnionFind(int iSize) :m_vNodeToRegion(iSize)

{

for (int i = 0; i < iSize; i++)

{

m_vNodeToRegion[i] = i;

}

m_iConnetRegionCount = iSize;

}

int GetConnectRegionIndex(int iNode)

{

int& iConnectNO = m_vNodeToRegion[iNode];

if (iNode == iConnectNO)

{

return iNode;

}

return iConnectNO = GetConnectRegionIndex(iConnectNO);

}

void Union(int iNode1, int iNode2)

{

const int iConnectNO1 = GetConnectRegionIndex(iNode1);

const int iConnectNO2 = GetConnectRegionIndex(iNode2);

if (iConnectNO1 == iConnectNO2)

{

return;

}

m_iConnetRegionCount–;

if (iConnectNO1 > iConnectNO2)

{

UnionConnect(iConnectNO1, iConnectNO2);

}

else

{

UnionConnect(iConnectNO2, iConnectNO1);

}

}

bool IsConnect(int iNode1, int iNode2)
{
  return GetConnectRegionIndex(iNode1) == GetConnectRegionIndex(iNode2);
}
int GetConnetRegionCount()const
{
  return m_iConnetRegionCount;
}
vector<int> GetNodeCountOfRegion()//各联通区域的节点数量
{
  const int iNodeSize = m_vNodeToRegion.size();
  vector<int> vRet(iNodeSize);
  for (int i = 0; i < iNodeSize; i++)
  {
    vRet[GetConnectRegionIndex(i)]++;
  }
  return vRet;
}

private:

void UnionConnect(int iFrom, int iTo)

{

m_vNodeToRegion[iFrom] = iTo;

}

vector m_vNodeToRegion;//各点所在联通区域的索引,本联通区域任意一点的索引,为了增加可理解性,用最小索引

int m_iConnetRegionCount;

};

class CUnionFindMST

{

public:

CUnionFindMST(const int iNodeSize) :m_uf(iNodeSize)

{

}
void AddEdge(const int iNode1, const int iNode2, int iWeight)
{
  if (m_uf.IsConnect(iNode1, iNode2))
  {
    return;
  }
  m_iMST += iWeight;
  m_uf.Union(iNode1, iNode2);
}
void AddEdge(const vector<int>& v)
{
  AddEdge(v[0], v[1], v[2]);
}
int MST()
{
  if (m_uf.GetConnetRegionCount() > 1)
  {
    return -1;
  }
  return m_iMST;
}

private:

int m_iMST = 0;

CUnionFind m_uf;

};

class CNearestMST

{

public:

CNearestMST(const int iNodeSize) :m_bDo(iNodeSize), m_vDis(iNodeSize, INT_MAX), m_vNeiTable(iNodeSize)

{

}
void Init(const vector<vector<int>>& edges)
{
  for (const auto& v : edges)
  {
    Add(v);
  }
}
void Add(const vector<int>& v)
{
  m_vNeiTable[v[0]].emplace_back(v[1], v[2]);
  m_vNeiTable[v[1]].emplace_back(v[0], v[2]);
}
int MST(int start)
{
  int next = start;
  while ((next = AddNode(next)) >= 0);
  return m_iMST;
}
int MST(int iNode1, int iNode2, int iWeight)
{
  m_bDo[iNode1] = true;
  for (const auto& it : m_vNeiTable[iNode1])
  {
    if (m_bDo[it.first])
    {
      continue;
    }
    m_vDis[it.first] = min(m_vDis[it.first], (long long)it.second);
  }
  m_iMST = iWeight;
  int next = iNode2;
  while ((next = AddNode(next)) >= 0);
  return m_iMST;
}

private:

int AddNode(int iCur)

{

m_bDo[iCur] = true;

for (const auto& it : m_vNeiTable[iCur])

{

if (m_bDo[it.first])

{

continue;

}

m_vDis[it.first] = min(m_vDis[it.first], (long long)it.second);

}

int iMinIndex = -1;
  for (int i = 0; i < m_vDis.size(); i++)
  {
    if (m_bDo[i])
    {
      continue;
    }
    if ((-1 == iMinIndex) || (m_vDis[i] < m_vDis[iMinIndex]))
    {
      iMinIndex = i;
    }
  }
  if (-1 != iMinIndex)
  {
    if (INT_MAX == m_vDis[iMinIndex])
    {
      m_iMST = -1;
      return -1;
    }
    m_iMST += m_vDis[iMinIndex];
  }
  return iMinIndex;
}
vector<bool> m_bDo;
vector<long long> m_vDis;
vector < vector<std::pair<int, int>>> m_vNeiTable;
long long m_iMST = 0;

};

typedef pair<long long, int> PAIRLLI;

class CDis

{

public:

static void Dis(vector& vDis, int start, const vector<vector<pair<int, int>>>& vNeiB)

{

std::priority_queue<PAIRLLI, vector, greater> minHeap;

minHeap.emplace(0, start);

while (minHeap.size())

{

const long long llDist = minHeap.top().first;

const int iCur = minHeap.top().second;

minHeap.pop();

if (-1 != vDis[iCur])

{

continue;

}

vDis[iCur] = llDist;

for (const auto& it : vNeiB[iCur])

{

minHeap.emplace(llDist + it.second, it.first);

}

}

}

};

class CNearestDis

{

public:

CNearestDis(int iSize) :m_iSize(iSize), DIS(m_vDis), PRE(m_vPre)

{

}
void Cal(int start, const vector<vector<pair<int, int>>>& vNeiB)
{
  m_vDis.assign(m_iSize, -1);
  m_vPre.assign(m_iSize, -1);
  vector<bool> vDo(m_iSize);//点是否已处理
  auto AddNode = [&](int iNode)
  {
    //const int iPreNode = m_vPre[iNode];
    long long llPreDis = m_vDis[iNode];
    vDo[iNode] = true;
    for (const auto& it : vNeiB[iNode])
    {
      if (vDo[it.first])
      {
        continue;
      }
      if ((-1 == m_vDis[it.first]) || (it.second + llPreDis < m_vDis[it.first]))
      {
        m_vDis[it.first] = it.second + llPreDis;
        m_vPre[it.first] = iNode;
      }
    }
    long long llMinDis = LLONG_MAX;
    int iMinIndex = -1;
    for (int i = 0; i < m_vDis.size(); i++)
    {
      if (vDo[i])
      {
        continue;
      }
      if (-1 == m_vDis[i])
      {
        continue;
      }
      if (m_vDis[i] < llMinDis)
      {
        iMinIndex = i;
        llMinDis = m_vDis[i];
      }
    }
    return (LLONG_MAX == llMinDis) ? -1 : iMinIndex;
  };
  int next = start;
  m_vDis[start] = 0;
  while (-1 != (next = AddNode(next)));
}
void Cal(const int start, vector<vector<int>>& edges)
{
  vector<vector<pair<int, int>>> vNeiB(m_iSize);
  for (int i = 0; i < edges.size(); i++)
  {
    const auto& v = edges[i];
    vNeiB[v[0]].emplace_back(v[1], v[2]);
    vNeiB[v[1]].emplace_back(v[0], v[2]);
  }
  Cal(start, vNeiB);
}
const vector<long long>& DIS;
const vector<int>& PRE;

private:

const int m_iSize;

vector m_vDis;//各点到起点的最短距离

vector m_vPre;//最短路径的前一点

};

class CNeiBo2

{

public:

CNeiBo2(int n, vector<vector>& edges, bool bDirect,int iBase=0)

{

m_vNeiB.resize(n);

for (const auto& v : edges)

{

m_vNeiB[v[0]- iBase].emplace_back(v[1]- iBase);

if (!bDirect)

{

m_vNeiB[v[1]- iBase].emplace_back(v[0]- iBase);

}

}

}

vector<vector> m_vNeiB;

};

class CNeiBo3

{

public:

CNeiBo3(int n, vector<vector>& edges, bool bDirect, int iBase = 0)

{

m_vNeiB.resize(n);

for (const auto& v : edges)

{

m_vNeiB[v[0] - iBase].emplace_back(v[1] - iBase,v[2]);

if (!bDirect)

{

m_vNeiB[v[1] - iBase].emplace_back(v[0] - iBase,v[2]);

}

}

}

vector<vector<std::pair<int,int>>> m_vNeiB;

};

struct SDecimal

{

SDecimal(int iNum = 0, int iDeno = 1)

{

m_iNum = iNum;

m_iDeno = iDeno;

int iGCD = GCD(abs(m_iNum), abs(m_iDeno));

m_iNum /= iGCD;

m_iDeno /= iGCD;

if (m_iDeno < 0)

{

m_iDeno = -m_iDeno;

m_iNum = -m_iNum;

}

}

SDecimal operator*(const SDecimal& o)const

{

return SDecimal(m_iNum * o.m_iNum, m_iDeno * o.m_iDeno);

}

SDecimal operator/(const SDecimal& o)const

{

return SDecimal(m_iNum * o.m_iDeno, m_iDeno * o.m_iNum);

}

SDecimal operator+(const SDecimal& o)const

{

const int iGCD = GCD(m_iDeno, o.m_iDeno);

const int iDeno = m_iDeno * o.m_iDeno / iGCD;

return SDecimal(m_iNum * (iDeno / m_iDeno) + o.m_iNum * (iDeno / o.m_iDeno), iDeno);

}

SDecimal operator-(const SDecimal& o)const

{

const int iGCD = GCD(m_iDeno, o.m_iDeno);

const int iDeno = m_iDeno * o.m_iDeno / iGCD;

return SDecimal(m_iNum * (iDeno / m_iDeno) - o.m_iNum * (iDeno / o.m_iDeno), iDeno);

}

bool operator==(const SDecimal& o)const

{

return (m_iNum == o.m_iNum) && (m_iDeno == o.m_iDeno);

}

bool operator<(const SDecimal& o)const

{

auto tmp = *this - o;

return tmp.m_iNum < 0;

}

int m_iNum = 0;//分子

int m_iDeno = 1;//分母

};

struct point {

double x, y;

point(double i, double j) :x(i), y(j) {}

};

//算两点距离

double dist(double x1, double y1, double x2, double y2) {

return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));

}

//计算圆心

point CircleCenter(point& a, point& b, int r) {

//算中点

point mid((a.x + b.x) / 2.0, (a.y + b.y) / 2.0);

//AB距离的一半

double d = dist(a.x, a.y, mid.x, mid.y);

//计算h

double h = sqrt(r * r - d * d);

//计算垂线

point ba(b.x - a.x, b.y - a.y);

point hd(-ba.y, ba.x);

double len = sqrt(hd.x * hd.x + hd.y * hd.y);

hd.x /= len, hd.y /= len;

hd.x *= h, hd.y *= h;

return point(hd.x + mid.x, hd.y + mid.y);

}

class C01LineTree

{

public:

C01LineTree(const vector& nums) :m_iEleSize(nums.size())

{

m_arr.resize(m_iEleSize * 4);

Init(nums, 1, 1, m_iEleSize);

m_vNeedFreshChilds.assign(m_iEleSize * 4, false);

}

void Rotato(int iLeftZeroIndex, int iRightZeroIndex)

{

int iRotatoLeft = iLeftZeroIndex + 1;

int iRotatoRight = iRightZeroIndex + 1;

Rotato(1, 1, m_iEleSize, iRotatoLeft, iRotatoRight);

}

int Query()

{

return m_arr[1];

}

private:

void Rotato(int iSaveIndex, int iDataBegin, int iDataEnd, int iRotatoLeft, int iRotatoRight)

{

if ((iRotatoLeft <= iDataBegin) && (iRotatoRight >= iDataEnd))

{//整个范围需要更新

RotatoSelf(iSaveIndex, iDataBegin, iDataEnd);

return;

}

int iMid = iDataBegin + (iDataEnd - iDataBegin) / 2;
  if (m_vNeedFreshChilds[iSaveIndex])
  {
    RotatoSelf(iSaveIndex * 2, iDataBegin, iMid);
    RotatoSelf(iSaveIndex * 2 + 1, iMid + 1, iDataEnd);
    m_vNeedFreshChilds[iSaveIndex] = false;
  }
  if (iMid >= iRotatoLeft)
  {
    Rotato(iSaveIndex * 2, iDataBegin, iMid, iRotatoLeft, iRotatoRight);
  }
  if (iMid + 1 <= iRotatoRight)
  {
    Rotato(iSaveIndex * 2 + 1, iMid + 1, iDataEnd, iRotatoLeft, iRotatoRight);
  }
  m_arr[iSaveIndex] = m_arr[iSaveIndex * 2] + m_arr[iSaveIndex * 2 + 1];
}
void RotatoSelf(int iSaveIndex, int iDataBegin, int iDataEnd)
{
  //总数量 - 翻转后0(翻转前1)的数量
  m_arr[iSaveIndex] = (iDataEnd - iDataBegin + 1) - m_arr[iSaveIndex];
  //懒惰法,标记本节点的子孙节点没更新
  m_vNeedFreshChilds[iSaveIndex] = !m_vNeedFreshChilds[iSaveIndex];
}
void Init(const vector<int>& nums, int iSaveIndex, int iDataBegin, int iDataEnd)
{
  if (iDataBegin == iDataEnd)
  {
    m_arr[iSaveIndex] = nums[iDataBegin - 1];
    return;
  }
  int iMid = iDataBegin + (iDataEnd - iDataBegin) / 2;
  Init(nums, iSaveIndex * 2, iDataBegin, iMid);
  Init(nums, iSaveIndex * 2 + 1, iMid + 1, iDataEnd);
  m_arr[iSaveIndex] = m_arr[iSaveIndex * 2] + m_arr[iSaveIndex * 2 + 1];
}
const int m_iEleSize;
vector<int> m_arr;
vector<bool> m_vNeedFreshChilds;

};

template<class ELE, class ResultType, ELE minEle, ELE maxEle>

class CLowUperr

{

public:

CLowUperr(int iResutlCount)

{

m_iResutlCount = iResutlCount;

m_vPre.assign(4, vector(iResutlCount));

}

void Init(const ELE* pLower, const ELE* pHigh, int iNum)

{

if (iNum <= 0)

{

return;

}

InitPre(pLower, pHigh);

iNum–;

while (iNum–)

{

pLower++;

pHigh++;

vector<vector> dp(4, vector(m_iResutlCount));

OnInitDP(dp);

//处理非边界

for (auto tmp = minEle; tmp <= maxEle; tmp++)

{

OnDo(dp[0], m_vPre[0], tmp);

}

//处理下边界

OnDo(dp[1], m_vPre[1], *pLower);

for (auto tmp = *pLower + 1; tmp <= maxEle; tmp++)

{

OnDo(dp[0], m_vPre[1], tmp );

}

//处理上边界

OnDo(dp[2], m_vPre[2], *pHigh );

for (auto tmp = minEle; tmp < *pHigh; tmp++)

{

OnDo(dp[0], m_vPre[2], tmp );

}

//处理上下边界

if (*pLower == *pHigh)

{

OnDo(dp[3], m_vPre[3], *pLower);

}

else

{

OnDo(dp[1], m_vPre[3], *pLower );

for (auto tmp = *pLower + 1; tmp < *pHigh; tmp++)

{

OnDo(dp[0], m_vPre[3], tmp );

}

OnDo(dp[2], m_vPre[3], *pHigh );

}

m_vPre.swap(dp);

}

}

ResultType Total(int iMinIndex, int iMaxIndex)

{

ResultType ret;

for (int status = 0; status < 4; status++)

{

for (int index = iMinIndex; index <= iMaxIndex; index++)

{

ret += m_vPre[status][index];

}

}

return ret;

}

protected:

int m_iResutlCount;
void InitPre(const ELE* const pLower, const ELE* const pHigh)
{
  for (ELE cur = *pLower; cur <= *pHigh; cur++)
  {
    int iStatus = 0;
    if (*pLower == cur)
    {
      iStatus = *pLower == *pHigh ? 3 : 1;
    }
    else if (*pHigh == cur)
    {
      iStatus = 2;
    }
    OnInitFirstEle(m_vPre[iStatus], cur);
  }
}
virtual void OnDo(vector<ResultType>& dp, const vector<ResultType>& vPre, ELE cur) = 0;
virtual void OnInitFirstEle(vector<ResultType>& vPre,const ELE curValue)
{
  int curIndex = curValue - minEle;
  if (curIndex < m_iResutlCount)
  {
    vPre[curIndex] = 1;
  }
}
virtual void OnInitDP(vector<vector<ResultType>>& dp)
{
}
vector<vector<ResultType>> m_vPre;

};

//马拉车计算回文回文

class CPalindrome

{

public:

//vOddHalfLen[i]表示 以s[i]为中心,且长度为奇数的最长回文的半长,包括s[i]

//比如:“aba” vOddHalfLen[1]为2 “abba” vEvenHalfLen[1]为2

static void CalHalfLen(vector& vOddHalfLen, vector& vEvenHalfLen, const string& s)

{

vector v;

for (const auto& ch : s)

{

v.emplace_back(ch);

v.emplace_back(‘*’);

}

v.pop_back();

const int len = v.size();
  vector<int> vHalfLen(len);
  int center = -1, r = -1;
  //center是对称中心,r是其右边界(闭)
  for (int i = 0; i < len; i++)
  {
    int tmp = 1;
    if (i <= r)
    {
      int pre = center - (i - center);
      tmp = min(vHalfLen[pre], r - i + 1);
    }
    for (tmp++; (i + tmp - 1 < len) && (i - tmp + 1 >= 0) && (v[i + tmp - 1] == v[i - tmp + 1]); tmp++);
    vHalfLen[i] = --tmp;
    const int iNewR = i + tmp - 1;
    if (iNewR > r)
    {
      r = iNewR;
      center = i;
    }
  }
  vOddHalfLen.resize(s.length());
  vEvenHalfLen.resize(s.length());
  for (int i = 0; i < len; i++)
  {
    if (i & 1)
    {
      vEvenHalfLen[i / 2] = vHalfLen[i] / 2;
    }
    else
    {
      vOddHalfLen[i / 2] = (vHalfLen[i] + 1) / 2;
    }
  }
}
//vOddLen[i]表示以i开始,奇数长度 最长回文
//vEvenLen[i]表示以i开始,偶数长度 最长回文
static void  CalLen(vector<int>& vOddLen, vector<int>& vEvenLen, const string& s)
{
  vector<char> v;
  for (const auto& ch : s)
  {
    v.emplace_back(ch);
    v.emplace_back('*');
  }
  v.pop_back();
  const int len = v.size();
  vector<int> vHalfLen(len);
  int center = -1, r = -1;
  //center是对称中心,r是其右边界(闭)
  for (int i = 0; i < len; i++)
  {
    int tmp = 1;
    if (i <= r)
    {
      int pre = center - (i - center);
      tmp = min(vHalfLen[pre], r - i + 1);
    }
    for (tmp++; (i + tmp - 1 < len) && (i - tmp + 1 >= 0) && (v[i + tmp - 1] == v[i - tmp + 1]); tmp++);
    vHalfLen[i] = --tmp;
    const int iNewR = i + tmp - 1;
    if (iNewR > r)
    {
      r = iNewR;
      center = i;
    }
  }
  vOddLen.resize(s.length());
  vEvenLen.resize(s.length());
  for (int i = 0; i < len; i++)
  {
    const int iHalfLen = (i & 1) ? (vHalfLen[i] / 2) : ((vHalfLen[i] + 1) / 2);
    const int left = i / 2 - iHalfLen + 1;
    if (i & 1)
    {
      vEvenLen[left] = vHalfLen[i] / 2*2;
    }
    else
    {
      vOddLen[left] = (vHalfLen[i] + 1) / 2*2-1;
    }
  }
}

};

//使用实例

//vector vOddHalfLen, vEvenHalfLen;

//CPalindrome::Do(vOddHalfLen, vEvenHalfLen, s);

class CKMP

{

public:

static vector Next(const string& s)

{

const int len = s.length();

vector vNext(len, -1);

for (int i = 1; i < len; i++)

{

int next = vNext[i - 1];

while ((-1 != next) && (s[next + 1] != s[i]))

{

next = vNext[next];

}

vNext[i] = next + (s[next + 1] == s[i]);

}

return vNext;

}

};

template

class CMergeSortIndex

{

public:

CMergeSortIndex(const vector& nums) :m_nums(nums)

{

m_c = nums.size();

m_vIndexs.resize(nums.size());

iota(m_vIndexs.begin(), m_vIndexs.end(), 0);

}

void SortIndex(int left, int right)

{

if (right - left <= 1)

{

return;

}

const int mid = left + (right - left) / 2;

SortIndex(left, mid);

SortIndex(mid, right);

OnSortLeftRightEnd(left, mid, right);

//nums的[left,mid) 和[mid,right)分别排序

m_vSortIndexs.clear();

int i1 = left, i2 = mid;

while ((i1 < mid) && (i2 < right))

{

if (m_nums[m_vIndexs[i1]] > m_nums[m_vIndexs[i2]])

{

m_vSortIndexs.emplace_back(m_vIndexs[i2++]);

}

else

{

m_vSortIndexs.emplace_back(m_vIndexs[i1]);

OnAdd1(i1++, i2, left, mid, right);

}

}

while (i1 < mid)

{

m_vSortIndexs.emplace_back(m_vIndexs[i1]);

OnAdd1(i1++, i2, left, mid, right);

}

while (i2 < right)

{

m_vSortIndexs.emplace_back(m_vIndexs[i2++]);

}

for (int i = 0; i < m_vSortIndexs.size(); i++)

{

m_vIndexs[i + left] = m_vSortIndexs[i];

}

}

vector Sort()

{

SortIndex(0, m_c);

vector vRet(m_c);

for (int i = 0; i < m_c; i++)

{

vRet[i] = m_nums[m_vIndexs[i]];

}

return vRet;

}

protected:

virtual void OnSortLeftRightEnd(int left, int mid, int right)

{

}
virtual void OnAdd1(int i1, int i2, int left, int mid, int right)
{
}
int m_c;
const vector<T>& m_nums;
vector<int> m_vIndexs;
vector<int> m_vSortIndexs;

};

template<class T = int, class _Pr = std::less >

class CTopK

{

public:

CTopK(int k) :m_iMinNum(k)

{

}
void Do(vector<T>& m_v, T* begin, int num)
{
  for (; num; begin++, num--)
  {
    while (m_v.size() && _Pr()(*begin, m_v.back()) && (m_iMinNum - m_v.size() + 1 <= num))
    {
      m_v.pop_back();
    }
    if (m_v.size() < m_iMinNum)
    {
      m_v.push_back(*begin);
    }
  }
}

protected:

const int m_iMinNum;

};

class CUnionFindDirect

{

public:

CUnionFindDirect(int iSize)

{

m_vRoot.resize(iSize);

iota(m_vRoot.begin(), m_vRoot.end(), 0);

}

void Connect(bool& bConflic, bool& bCyc, int iFrom, int iTo)

{

bConflic = bCyc = false;

if (iFrom != m_vRoot[iFrom])

{

bConflic = true;

}

Fresh(iTo);
  if (m_vRoot[iTo] == iFrom)
  {
    bCyc = true;
  }
  if (bConflic || bCyc)
  {
    return;
  }
  m_vRoot[iFrom] = m_vRoot[iTo];
}

private:

int Fresh(int iNode)

{

if (m_vRoot[iNode] == iNode)

{

return iNode;

}

return m_vRoot[iNode] = Fresh(m_vRoot[iNode]);

}

vector m_vRoot;

};

#define MACRO_BEGIN_END(n) n.begin(),n.end()

#define MacroTopSort(que,vNeiBo)

while (que.size())

{

const int cur = que.front();

que.pop();

for (const auto& next : vNeiBo[cur])

{

vDeg[next]–;

if (1 == vDeg[next])

{


}

}

}

#define Macro2DBFS(queRowCol,m_r,m_c)

queue<pair<int, int>> queRowCol;

vector<vector> vDis(m_r, vector(m_c, -1));

while (queRowCol.size())

{

const auto [r, c] = queRowCol.front();

queRowCol.pop();

auto Move = [&vDis, &queRowCol, this](int r, int c, int iDis)

{

if ((r < 0) || (r >= m_r))

{

return;

}

if ((c < 0) || (c >= m_c))

{

return;

}

if (-1 != vDis[r][c])

{

return;

}

vDis[r][c] = iDis;

queRowCol.emplace(r, c);

};

const int iDis = vDis[r][c] + 1;

Move(r + 1, c, iDis);

Move(r - 1, c, iDis);

Move(r, c + 1, iDis);

Move(r, c - 1, iDis);

}

/*

struct TreeNode {

int val;

TreeNode *left;

TreeNode *right;

TreeNode(int x) : val(x), left(NULL), right(NULL) {}

TreeNode(int x, int iLeft) : val(x), left(new TreeNode(iLeft)), right(nullptr) {}

TreeNode(int x, int iLeft, int iRghit) : val(x), left(new TreeNode(iLeft)), right(new TreeNode(iRghit)) {}

};

namespace NTree

{

TreeNode* Init(const vector& nums, int iNull = 10000)

{

if (0 == nums.size())

{

return nullptr;

}

vector<TreeNode*> ptrs(nums.size() + 1), ptrParent(1);

for (int i = 0; i < nums.size(); i++)

{

if (iNull == nums[i])

{

continue;

}

const int iNO = i + 1;

ptrs[iNO] = new TreeNode(nums[i]);

ptrParent.emplace_back(ptrs[iNO]);

if (1 == iNO)

{

continue;

}

if (iNO & 1)

{//奇数是右支

ptrParent[iNO / 2]->right = ptrs[iNO];

}

else

{

ptrParent[iNO / 2]->left = ptrs[iNO];

}

}

return ptrs[1];

}

}

*/

class CGoodString : public CLowUperr<char, C1097Int<>, ‘a’, ‘z’>

{

public:

CGoodString(string evil):CLowUperr<char, C1097Int<>, ‘a’, ‘z’>(evil.size())

{

m_c = evil.size();

m_strEvil = evil;

m_vMaxLen.assign(m_c, 0);

for (int i = 1; i < m_c; i++)

{

int iPreSameLen = m_vMaxLen[i-1];

while (evil[iPreSameLen] != evil[i])

{

if (0 == iPreSameLen)

{

break;

}

iPreSameLen = m_vMaxLen[iPreSameLen-1];

}

m_vMaxLen[i] = iPreSameLen+(evil[iPreSameLen] == evil[i]);

}

}

protected:

void OnDo(vector<C1097Int<>>& dp, const vector<C1097Int<>>& vPre, char cur)override

{

for (int i = 0; i < m_c; i++)

{

if (0 == vPre[i].ToInt())

{

continue;

}

int preSameLen = i;

while (m_strEvil[preSameLen] != cur)

{

if (0 == preSameLen)

{

break;

}

preSameLen = m_vMaxLen[preSameLen - 1];

}

const int curSameLen = preSameLen + (m_strEvil[preSameLen] == cur);

if (curSameLen == m_c)

{

continue;

}

dp[curSameLen] += vPre[i];

}

}

void OnInitFirstEle(vector<C1097Int<>>& vPre, const char curValue)override

{

int iSameLen = m_strEvil[0] == curValue;

if (iSameLen < m_c)

{

vPre[iSameLen] += 1;

}

}

string m_strEvil;

vector m_vMaxLen;//m_vNext[i] 记录 evil[0]到evil[i] 的最长公共前后缀

int m_c;

};

class Solution {

public:

int findGoodStrings(int n, string s1, string s2, string evil) {

CGoodString gs(evil);

gs.Init(s1.data(), s2.data(), s1.length());

return gs.Total(0, evil.size() - 1).ToInt();

}

int m_c;

};


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