#include <bits/stdc++.h>
char str[100001];
std::vector<int> pos[2][100001];
int last[26];
int n;
struct info {
  int num, dis;
  long long ans;
};
info merge(info a, info b) {
  if (!a.num) return b;
  if (!b.num) return a;
  return (info){a.num + b.num, a.dis + b.dis,
                1ll * b.num * a.dis + a.ans + b.ans};
}
int Log[100001];
struct bl {
  int s[100001], pos[100001][26], nxt[100001][17], Next[100001];
  int st[100001][17];
  int q[100001], h, t, last[26];
  info val[100001][17];
  bool rev;
  int query(int l, int r) {
    int k = Log[r - l + 1];
    return std::max(st[l][k], st[r - (1 << k) + 1][k]);
  }
  void init() {
    for (int i = 0; i < 26; i++) last[i] = n;
    for (int i = n; i; i--) {
      Next[i] = last[s[i]];
      last[s[i]] = i;
    }
    for (int i = 0; i < 26; i++) last[i] = 0;
    for (int i = 1; i <= n; i++) st[i][0] = Next[i];
    for (int j = 1; (1 << j) <= n; j++)
      for (int i = 1; i + (1 << j) - 1 <= n; i++)
        st[i][j] = std::max(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
    for (int i = 1; i <= n; i++) {
      nxt[i][0] = query(last[s[i]], i);
      val[i][0] = (info){nxt[i][0] - i, 1, nxt[i][0] - i};
      last[s[i]] = i;
    }
    for (int j = 1; j <= 16; j++)
      for (int i = 1; i <= n; i++)
        nxt[i][j] = nxt[nxt[i][j - 1]][j - 1],
        val[i][j] = merge(val[i][j - 1], val[nxt[i][j - 1]][j - 1]);
  }
} front, back;
int main() {
  scanf("%s", str + 1);
  n = strlen(str + 1);
  Log[1] = 0;
  for (int i = 2; i <= n; i++) Log[i] = Log[i >> 1] + 1;
  for (int i = 1; i <= n; i++) front.s[i] = back.s[n - i + 1] = str[i] - 'a';
  front.init();
  back.init();
  for (int i = 1; i <= n; i++) {
    last[str[i] - 'a'] = i;
    for (int j = 0; j < 26; j++) pos[0][i].push_back(last[j]);
    pos[0][i].push_back(0);
  }
  for (int i = 0; i < 26; i++) last[i] = n + 1;
  for (int i = n; i; i--) {
    last[str[i] - 'a'] = i;
    for (int j = 0; j < 26; j++) pos[1][i].push_back(last[j]);
    pos[1][i].push_back(n + 1);
  }
  long long tot = 0;
  for (int i = 1; i <= n; i++) {
    int L = i, R = i;
    info ansL = (info){0, 0, 0}, ansR = (info){0, 0, 0};
    std::sort(pos[0][i].begin(), pos[0][i].end());
    std::sort(pos[1][i].begin(), pos[1][i].end());
    std::reverse(pos[1][i].begin(), pos[1][i].end());
    for (; L > 1 || R < n;) {
      while (L <= pos[0][i].back() || R >= pos[1][i].back()) {
        while (L <= pos[0][i].back()) pos[0][i].pop_back();
        while (R >= pos[1][i].back()) pos[1][i].pop_back();
        int nR = front.query(L, R),
            nL = n + 1 - back.query(n - R + 1, n - L + 1);
        ansL = merge(ansL, (info){L - nL, 1, L - nL});
        ansR = merge(ansR, (info){nR - R, 1, nR - R});
        L = nL, R = nR;
      }
      for (int j = 16; ~j; --j)
        if (front.nxt[R][j] < pos[1][i].back() &&
            n + 1 - back.nxt[n - L + 1][j] > pos[0][i].back())
          ansL = merge(ansL, back.val[n - L + 1][j]),
          ansR = merge(ansR, front.val[R][j]), R = front.nxt[R][j],
          L = n + 1 - back.nxt[n - L + 1][j];
      if (L > pos[0][i].back() && R < pos[1][i].back()) {
        ansL = merge(ansL, back.val[n - L + 1][0]),
        ansR = merge(ansR, front.val[R][0]), R = front.nxt[R][0],
        L = n + 1 - back.nxt[n - L + 1][0];
      }
    }
    tot += ansL.ans + ansR.ans;
  }
  printf("%lld\n", tot);
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

There is a string s of lowercase English letters. A cursor is positioned on one of the characters. The cursor can be moved with the following operation: choose a letter c and a direction (left or right). The cursor is then moved to the closest occurence of c in the chosen direction. If there is no letter c in that direction, the cursor stays in place. For example, if s = abaab with the cursor on the second character (a[b]aab), then:

  * moving to the closest letter a to the left places the cursor on the first character ([a]baab);
  * moving to the closest letter a to the right places the cursor the third character (ab[a]ab);
  * moving to the closest letter b to the right places the cursor on the fifth character (abaa[b]);
  * any other operation leaves the cursor in place.



Let dist(i, j) be the smallest number of operations needed to move the cursor from the i-th character to the j-th character. Compute \displaystyle ∑_{i = 1}^n ∑_{j = 1}^n dist(i, j).

Input

The only line contains a non-empty string s of at most 10^5 lowercase English letters.

Output

Print a single integer \displaystyle ∑_{i = 1}^n ∑_{j = 1}^n dist(i, j).

Examples

Input


abcde


Output


20


Input


abacaba


Output


58

Note

In the first sample case, dist(i, j) = 0 for any pair i = j, and 1 for all other pairs.

### Response

```cpp
#include <bits/stdc++.h>
char str[100001];
std::vector<int> pos[2][100001];
int last[26];
int n;
struct info {
  int num, dis;
  long long ans;
};
info merge(info a, info b) {
  if (!a.num) return b;
  if (!b.num) return a;
  return (info){a.num + b.num, a.dis + b.dis,
                1ll * b.num * a.dis + a.ans + b.ans};
}
int Log[100001];
struct bl {
  int s[100001], pos[100001][26], nxt[100001][17], Next[100001];
  int st[100001][17];
  int q[100001], h, t, last[26];
  info val[100001][17];
  bool rev;
  int query(int l, int r) {
    int k = Log[r - l + 1];
    return std::max(st[l][k], st[r - (1 << k) + 1][k]);
  }
  void init() {
    for (int i = 0; i < 26; i++) last[i] = n;
    for (int i = n; i; i--) {
      Next[i] = last[s[i]];
      last[s[i]] = i;
    }
    for (int i = 0; i < 26; i++) last[i] = 0;
    for (int i = 1; i <= n; i++) st[i][0] = Next[i];
    for (int j = 1; (1 << j) <= n; j++)
      for (int i = 1; i + (1 << j) - 1 <= n; i++)
        st[i][j] = std::max(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
    for (int i = 1; i <= n; i++) {
      nxt[i][0] = query(last[s[i]], i);
      val[i][0] = (info){nxt[i][0] - i, 1, nxt[i][0] - i};
      last[s[i]] = i;
    }
    for (int j = 1; j <= 16; j++)
      for (int i = 1; i <= n; i++)
        nxt[i][j] = nxt[nxt[i][j - 1]][j - 1],
        val[i][j] = merge(val[i][j - 1], val[nxt[i][j - 1]][j - 1]);
  }
} front, back;
int main() {
  scanf("%s", str + 1);
  n = strlen(str + 1);
  Log[1] = 0;
  for (int i = 2; i <= n; i++) Log[i] = Log[i >> 1] + 1;
  for (int i = 1; i <= n; i++) front.s[i] = back.s[n - i + 1] = str[i] - 'a';
  front.init();
  back.init();
  for (int i = 1; i <= n; i++) {
    last[str[i] - 'a'] = i;
    for (int j = 0; j < 26; j++) pos[0][i].push_back(last[j]);
    pos[0][i].push_back(0);
  }
  for (int i = 0; i < 26; i++) last[i] = n + 1;
  for (int i = n; i; i--) {
    last[str[i] - 'a'] = i;
    for (int j = 0; j < 26; j++) pos[1][i].push_back(last[j]);
    pos[1][i].push_back(n + 1);
  }
  long long tot = 0;
  for (int i = 1; i <= n; i++) {
    int L = i, R = i;
    info ansL = (info){0, 0, 0}, ansR = (info){0, 0, 0};
    std::sort(pos[0][i].begin(), pos[0][i].end());
    std::sort(pos[1][i].begin(), pos[1][i].end());
    std::reverse(pos[1][i].begin(), pos[1][i].end());
    for (; L > 1 || R < n;) {
      while (L <= pos[0][i].back() || R >= pos[1][i].back()) {
        while (L <= pos[0][i].back()) pos[0][i].pop_back();
        while (R >= pos[1][i].back()) pos[1][i].pop_back();
        int nR = front.query(L, R),
            nL = n + 1 - back.query(n - R + 1, n - L + 1);
        ansL = merge(ansL, (info){L - nL, 1, L - nL});
        ansR = merge(ansR, (info){nR - R, 1, nR - R});
        L = nL, R = nR;
      }
      for (int j = 16; ~j; --j)
        if (front.nxt[R][j] < pos[1][i].back() &&
            n + 1 - back.nxt[n - L + 1][j] > pos[0][i].back())
          ansL = merge(ansL, back.val[n - L + 1][j]),
          ansR = merge(ansR, front.val[R][j]), R = front.nxt[R][j],
          L = n + 1 - back.nxt[n - L + 1][j];
      if (L > pos[0][i].back() && R < pos[1][i].back()) {
        ansL = merge(ansL, back.val[n - L + 1][0]),
        ansR = merge(ansR, front.val[R][0]), R = front.nxt[R][0],
        L = n + 1 - back.nxt[n - L + 1][0];
      }
    }
    tot += ansL.ans + ansR.ans;
  }
  printf("%lld\n", tot);
}

```