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;
struct state {
  int link, go[26], max_l;
  bool term, used;
  long long ans, sum;
  int &operator[](int ind) { return go[ind]; }
};
const int max_l = 1000000;
state states[max_l];
char s[max_l];
int last = 0, freeS = 1;
void extend(int c) {
  int add = freeS++;
  memset(states[add].go, -1, sizeof(states[add].go));
  states[add].max_l = states[last].max_l + 1;
  int i = last;
  while ((i != -1) && (states[i][c] == -1))
    states[i][c] = add, i = states[i].link;
  if (i == -1)
    states[add].link = 0;
  else {
    int q = states[i][c];
    if (states[q].max_l == states[i].max_l + 1)
      states[add].link = q;
    else {
      int clone = freeS++;
      states[clone] = states[q];
      states[clone].max_l = states[i].max_l + 1;
      while ((i != -1) && (states[i][c] == q))
        states[i][c] = clone, i = states[i].link;
      states[q].link = states[add].link = clone;
    }
  }
  last = add;
}
long long dfs(int v) {
  if (states[v].used) return states[v].sum;
  states[v].used = true;
  states[v].ans = (int)states[v].term;
  states[v].sum = 0;
  for (int c = 0; c < 26; ++c)
    if (states[v][c] != -1) {
      states[v].sum += dfs(states[v][c]);
      states[v].ans += states[states[v][c]].ans;
    }
  states[v].sum +=
      (v == 0) ? 0 : (states[v].ans * 1ll * (states[v].ans + 1)) / 2;
  return states[v].sum;
}
int main() {
  memset(states[0].go, -1, sizeof(states[0].go));
  states[0].max_l = 0;
  states[0].link = -1;
  scanf("%s", s);
  int n = strlen(s);
  for (int i = 0; i < n; ++i) extend(s[i] - 'a');
  while (last != 0) {
    states[last].term = true;
    last = states[last].link;
  }
  cout << dfs(0) << endl;
  return 0;
}