#include <bits/stdc++.h>
using namespace std;
namespace Fast_IO {
const int MAXL((1 << 18) + 1);
int iof, iotp;
char ioif[MAXL], *ioiS, *ioiT, ioof[MAXL],
    *iooS = ioof, *iooT = ioof + MAXL - 1, ioc, iost[55];
char Getchar() {
  if (ioiS == ioiT) {
    ioiS = ioif;
    ioiT = ioiS + fread(ioif, 1, MAXL, stdin);
    return (ioiS == ioiT ? EOF : *ioiS++);
  } else
    return (*ioiS++);
}
void Write() {
  fwrite(ioof, 1, iooS - ioof, stdout);
  iooS = ioof;
}
void Putchar(char x) {
  *iooS++ = x;
  if (iooS == iooT) Write();
}
inline int read() {
  int x = 0;
  for (iof = 1, ioc = Getchar(); (ioc < '0' || ioc > '9') && ioc != EOF;)
    iof = ioc == '-' ? -1 : 1, ioc = Getchar();
  if (ioc == EOF) exit(0);
  for (x = 0; ioc <= '9' && ioc >= '0'; ioc = Getchar())
    x = (x << 3) + (x << 1) + (ioc ^ 48);
  return x * iof;
}
inline long long read_ll() {
  long long x = 0;
  for (iof = 1, ioc = Getchar(); (ioc < '0' || ioc > '9') && ioc != EOF;)
    iof = ioc == '-' ? -1 : 1, ioc = Getchar();
  if (ioc == EOF) exit(0);
  for (x = 0; ioc <= '9' && ioc >= '0'; ioc = Getchar())
    x = (x << 3) + (x << 1) + (ioc ^ 48);
  return x * iof;
}
template <class Int>
void Print(Int x, char ch = '\0') {
  if (!x) Putchar('0');
  if (x < 0) Putchar('-'), x = -x;
  while (x) iost[++iotp] = x % 10 + '0', x /= 10;
  while (iotp) Putchar(iost[iotp--]);
  if (ch) Putchar(ch);
}
void Getstr(char *s, int &l) {
  for (ioc = Getchar(); ioc == ' ' || ioc == '\n' || ioc == '\t';)
    ioc = Getchar();
  if (ioc == EOF) exit(0);
  for (l = 0; !(ioc == ' ' || ioc == '\n' || ioc == '\t' || ioc == EOF);
       ioc = Getchar())
    s[l++] = ioc;
  s[l] = 0;
}
void Putstr(const char *s) {
  for (int i = 0, n = strlen(s); i < n; ++i) Putchar(s[i]);
}
}  // namespace Fast_IO
using namespace Fast_IO;
const int MAX = 1e5 + 50;
const long long MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3f;
const double EPS = 1e-6;
long long qpow(long long a, long long n) {
  long long res = 1LL;
  while (n) {
    if (n & 1) res = res * a % MOD;
    a = a * a % MOD;
    n >>= 1;
  }
  return res;
}
long long qpow(long long a, long long n, long long p) {
  a %= p;
  long long res = 1LL;
  while (n) {
    if (n & 1) res = res * a % p;
    a = a * a % p;
    n >>= 1;
  }
  return res;
}
long long npow(long long a, long long n) {
  long long res = 1LL;
  while (n) {
    if (n & 1) res = res * a;
    a = a * a;
    n >>= 1;
    if (res < 0 || a < 0) return 0;
  }
  return res;
}
long long inv(long long a) { return qpow(a, MOD - 2); }
long long inv(long long a, long long p) { return qpow(a, p - 2, p); }
int last[30];
long long dp[30];
string ss;
int main() {
  cin >> ss;
  ss = " " + ss;
  int mx = 0;
  for (int i = 1; i < ss.size(); ++i) {
    set<int> S;
    last[ss[i] - 'a'] = i;
    for (int j = 0; j < 26; ++j) {
      if (last[j] != 0) S.insert(-last[j]);
    }
    S.insert(0);
    int la = i + 1;
    int cnt = 0;
    for (auto it : S) {
      cnt++;
      dp[cnt] += la + it;
      la = -it;
      mx = max(mx, cnt);
    }
  }
  cout << mx - 1 << endl;
  for (int i = 2; i <= mx; ++i) cout << dp[i] << endl;
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

String diversity is the number of symbols that occur in the string at least once. Diversity of s will be denoted by d(s). For example , d("aaa")=1, d("abacaba")=3.

Given a string s, consisting of lowercase Latin letters. Consider all its substrings. Obviously, any substring diversity is a number from 1 to d(s). Find statistics about substrings diversity: for each k from 1 to d(s), find how many substrings of s has a diversity of exactly k.

Input

The input consists of a single line containing s. It contains only lowercase Latin letters, the length of s is from 1 to 3·105.

Output

Print to the first line the value d(s). Print sequence t1, t2, ..., td(s) to the following lines, where ti is the number of substrings of s having diversity of exactly i.

Examples

Input

abca


Output

3
4
3
3


Input

aabacaabbad


Output

4
14
19
28
5

Note

Consider the first example.

We denote by s(i, j) a substring of "abca" with the indices in the segment [i, j].

  * s(1, 1) =  "a", d("a") = 1
  * s(2, 2) =  "b", d("b") = 1
  * s(3, 3) =  "c", d("c") = 1
  * s(4, 4) =  "a", d("a") = 1
  * s(1, 2) =  "ab", d("ab") = 2
  * s(2, 3) =  "bc", d("bc") = 2
  * s(3, 4) =  "ca", d("ca") = 2
  * s(1, 3) =  "abc", d("abc") = 3
  * s(2, 4) =  "bca", d("bca") = 3
  * s(1, 4) =  "abca", d("abca") = 3



Total number of substring with diversity 1 is 4, with diversity 2 equals 3, 3 diversity is 3.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
namespace Fast_IO {
const int MAXL((1 << 18) + 1);
int iof, iotp;
char ioif[MAXL], *ioiS, *ioiT, ioof[MAXL],
    *iooS = ioof, *iooT = ioof + MAXL - 1, ioc, iost[55];
char Getchar() {
  if (ioiS == ioiT) {
    ioiS = ioif;
    ioiT = ioiS + fread(ioif, 1, MAXL, stdin);
    return (ioiS == ioiT ? EOF : *ioiS++);
  } else
    return (*ioiS++);
}
void Write() {
  fwrite(ioof, 1, iooS - ioof, stdout);
  iooS = ioof;
}
void Putchar(char x) {
  *iooS++ = x;
  if (iooS == iooT) Write();
}
inline int read() {
  int x = 0;
  for (iof = 1, ioc = Getchar(); (ioc < '0' || ioc > '9') && ioc != EOF;)
    iof = ioc == '-' ? -1 : 1, ioc = Getchar();
  if (ioc == EOF) exit(0);
  for (x = 0; ioc <= '9' && ioc >= '0'; ioc = Getchar())
    x = (x << 3) + (x << 1) + (ioc ^ 48);
  return x * iof;
}
inline long long read_ll() {
  long long x = 0;
  for (iof = 1, ioc = Getchar(); (ioc < '0' || ioc > '9') && ioc != EOF;)
    iof = ioc == '-' ? -1 : 1, ioc = Getchar();
  if (ioc == EOF) exit(0);
  for (x = 0; ioc <= '9' && ioc >= '0'; ioc = Getchar())
    x = (x << 3) + (x << 1) + (ioc ^ 48);
  return x * iof;
}
template <class Int>
void Print(Int x, char ch = '\0') {
  if (!x) Putchar('0');
  if (x < 0) Putchar('-'), x = -x;
  while (x) iost[++iotp] = x % 10 + '0', x /= 10;
  while (iotp) Putchar(iost[iotp--]);
  if (ch) Putchar(ch);
}
void Getstr(char *s, int &l) {
  for (ioc = Getchar(); ioc == ' ' || ioc == '\n' || ioc == '\t';)
    ioc = Getchar();
  if (ioc == EOF) exit(0);
  for (l = 0; !(ioc == ' ' || ioc == '\n' || ioc == '\t' || ioc == EOF);
       ioc = Getchar())
    s[l++] = ioc;
  s[l] = 0;
}
void Putstr(const char *s) {
  for (int i = 0, n = strlen(s); i < n; ++i) Putchar(s[i]);
}
}  // namespace Fast_IO
using namespace Fast_IO;
const int MAX = 1e5 + 50;
const long long MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3f;
const double EPS = 1e-6;
long long qpow(long long a, long long n) {
  long long res = 1LL;
  while (n) {
    if (n & 1) res = res * a % MOD;
    a = a * a % MOD;
    n >>= 1;
  }
  return res;
}
long long qpow(long long a, long long n, long long p) {
  a %= p;
  long long res = 1LL;
  while (n) {
    if (n & 1) res = res * a % p;
    a = a * a % p;
    n >>= 1;
  }
  return res;
}
long long npow(long long a, long long n) {
  long long res = 1LL;
  while (n) {
    if (n & 1) res = res * a;
    a = a * a;
    n >>= 1;
    if (res < 0 || a < 0) return 0;
  }
  return res;
}
long long inv(long long a) { return qpow(a, MOD - 2); }
long long inv(long long a, long long p) { return qpow(a, p - 2, p); }
int last[30];
long long dp[30];
string ss;
int main() {
  cin >> ss;
  ss = " " + ss;
  int mx = 0;
  for (int i = 1; i < ss.size(); ++i) {
    set<int> S;
    last[ss[i] - 'a'] = i;
    for (int j = 0; j < 26; ++j) {
      if (last[j] != 0) S.insert(-last[j]);
    }
    S.insert(0);
    int la = i + 1;
    int cnt = 0;
    for (auto it : S) {
      cnt++;
      dp[cnt] += la + it;
      la = -it;
      mx = max(mx, cnt);
    }
  }
  cout << mx - 1 << endl;
  for (int i = 2; i <= mx; ++i) cout << dp[i] << endl;
  return 0;
}

```