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;
int f[200010];
struct Suffix_Automata {
  int minlen[200010], maxlen[200010], trans[200010][26], link[200010], Size,
      Last;
  Suffix_Automata() { Size = Last = 1; }
  inline void extend(int id) {
    int cur = ++Size, p;
    f[Size] = 1;
    maxlen[cur] = maxlen[Last] + 1;
    for (p = Last; p && !trans[p][id]; p = link[p]) trans[p][id] = cur;
    if (!p)
      link[cur] = 1;
    else {
      int q = trans[p][id];
      if (maxlen[q] == maxlen[p] + 1)
        link[cur] = q;
      else {
        int clone = (++Size);
        maxlen[clone] = maxlen[p] + 1;
        for (int t = 0; t < 26; ++t) trans[clone][t] = trans[q][t];
        link[clone] = link[q];
        for (; p && trans[p][id] == q; p = link[p]) trans[p][id] = clone;
        link[cur] = link[q] = clone;
      }
    }
    Last = cur;
  }
};
struct edge {
  int pre, to;
} ed[200010];
int head[200010], cnt;
void merge(int a, int b) {
  cnt++;
  ed[cnt].pre = head[a];
  ed[cnt].to = b;
  head[a] = cnt;
}
Suffix_Automata SAM;
char s[200010];
long long ans;
void dfs(int x) {
  for (int t = head[x]; t; t = ed[t].pre) {
    int l = ed[t].to;
    dfs(l);
    f[x] += f[l];
  }
  if (x > 1)
    ans += 1LL * (SAM.maxlen[x] - SAM.minlen[x] + 1) * f[x] * (f[x] + 1) / 2;
}
int main() {
  scanf("%s", s);
  int gg = strlen(s);
  for (int t = 0; t < gg; ++t) SAM.extend(s[t] - 'a');
  for (int t = 2; t <= SAM.Size; ++t) {
    merge(SAM.link[t], t);
    SAM.minlen[t] = SAM.maxlen[SAM.link[t]] + 1;
  }
  dfs(1);
  printf("%lld", ans);
}