Problem: You are given a string s. Each pair of numbers l and r that fulfill the condition 1 ≤ l ≤ r ≤ |s|, correspond to a substring of the string s, starting in the position l and ending in the position r (inclusive).

Let's define the function of two strings F(x, y) like this. We'll find a list of such pairs of numbers for which the corresponding substrings of string x are equal to string y. Let's sort this list of pairs according to the pair's first number's increasing. The value of function F(x, y) equals the number of non-empty continuous sequences in the list.

For example: F(babbabbababbab, babb) = 6. The list of pairs is as follows:

(1, 4), (4, 7), (9, 12)

Its continuous sequences are: 

  * (1, 4)
  * (4, 7)
  * (9, 12)
  * (1, 4), (4, 7)
  * (4, 7), (9, 12)
  * (1, 4), (4, 7), (9, 12)



Your task is to calculate for the given string s the sum F(s, x) for all x, that x belongs to the set of all substrings of a string s.

Input

The only line contains the given string s, consisting only of small Latin letters (1 ≤ |s| ≤ 105).

Output

Print the single number — the sought sum.

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.

Examples

Input

aaaa


Output

20


Input

abcdef


Output

21


Input

abacabadabacaba


Output

188

Note

In the first sample the function values at x equal to "a", "aa", "aaa" and "aaaa" equal 10, 6, 3 and 1 correspondingly.

In the second sample for any satisfying x the function value is 1.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
char s[100010];
int n;
long long ans;
template <typename T>
void chkmin(T &x, T y) {
  x = min(x, y);
}
template <typename T>
void chkmax(T &x, T y) {
  x = max(x, y);
}
template <typename T>
void read(T &x) {
  x = 0;
  int f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  x *= f;
}
struct Suffix_Automaton {
  int n, cnt, root, last;
  struct info {
    int son[26], dep, fa, size;
  } a[100010 * 2];
  vector<int> b[100010 * 2];
  int creat(int depth) {
    ++cnt;
    a[cnt].dep = depth;
    return cnt;
  }
  void extend(int ch) {
    int p = last, np = creat(a[p].dep + 1);
    while (a[p].son[ch] == 0) {
      a[p].son[ch] = np;
      p = a[p].fa;
    }
    if (a[p].son[ch] == np)
      a[np].fa = root;
    else {
      int q = a[p].son[ch];
      if (a[q].dep == a[p].dep + 1)
        a[np].fa = q;
      else {
        int nq = creat(a[p].dep + 1);
        memcpy(a[nq].son, a[q].son, sizeof(a[q].son));
        a[nq].fa = a[q].fa;
        a[q].fa = a[np].fa = nq;
        while (a[p].son[ch] == q) {
          a[p].son[ch] = nq;
          p = a[p].fa;
        }
      }
    }
    ++a[last = np].size;
  }
  void init(char *s) {
    cnt = root = last = 0;
    n = strlen(s + 1);
    for (int i = 1; i <= n; ++i) extend(s[i] - 'a');
  }
  void dfs(int pos) {
    for (unsigned i = 0, si = b[pos].size(); i < si; ++i) {
      int son = b[pos][i];
      dfs(son);
      a[pos].size += a[son].size;
    }
    long long tmp = a[pos].size;
    tmp = tmp * (1 + tmp) / 2;
    ans = ans + tmp * (a[pos].dep - a[a[pos].fa].dep);
  }
  void work() {
    for (int i = 1; i <= cnt; ++i) b[a[i].fa].push_back(i);
    dfs(0);
  }
} sam;
int main() {
  scanf("%s", s + 1);
  sam.init(s);
  sam.work();
  printf("%I64d\n", ans);
  return 0;
}