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;
using ll = long long;
inline int read();
const int M = 100016, MOD = 1000000007;
int sz, lst;
int ch[M << 1][128], len[M << 1], link[M << 1], cnt[M << 1];
int firstpos[M << 1], lastpos[M << 1];
void extend(const char *s) {
  for (int i = 0; s[i]; ++i) {
    int c = s[i];
    int cur = ++sz;
    len[cur] = len[lst] + 1;
    int p = lst;
    while (!ch[p][c]) {
      ch[p][c] = cur;
      p = link[p];
    }
    if (ch[p][c] != cur) {
      int q = ch[p][c];
      if (len[p] + 1 == len[q])
        link[cur] = q;
      else {
        int clone = ++sz;
        memcpy(ch[clone], ch[q], sizeof(ch[q]));
        link[clone] = link[q];
        firstpos[clone] = firstpos[q];
        lastpos[clone] = lastpos[q];
        len[clone] = len[p] + 1;
        while (ch[p][c] == q) {
          ch[p][c] = clone;
          p = link[p];
        }
        link[q] = link[cur] = clone;
      }
    }
    lst = cur;
    ++cnt[cur];
    firstpos[cur] = lastpos[cur] = i;
  }
  vector<int> nodes;
  for (int i = 1; i <= sz; ++i) nodes.push_back(i);
  sort(nodes.begin(), nodes.end(),
       [&](int a, int b) { return len[a] > len[b]; });
  for (auto u : nodes) cnt[link[u]] += cnt[u];
}
char tex[M];
int main(void) {
  scanf("%s", tex);
  extend(tex);
  ll ans = 0;
  for (int i = 1; i <= sz; ++i)
    ans += 1ll * cnt[i] * (cnt[i] + 1) / 2 * (len[i] - len[link[i]]);
  printf("%I64d\n", ans);
  return 0;
}
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}