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;
const int md = 1e9 + 7;
const int maxn = 1e5 + 5;
const int Size = maxn * 2;
namespace SAM {
int nxt[Size][27];
int par[Size];
int len[Size];
int cur[Size];
int pos[Size];
int g[Size];
int rt, last, tol;
int newNode(int x) {
  len[++tol] = x;
  par[tol] = 0;
  memset(nxt[tol], 0, sizeof nxt[tol]);
  return tol;
}
void init() {
  tol = 0;
  last = rt = newNode(0);
}
void add(int c) {
  int p = last;
  int np = newNode(len[p] + 1);
  while (p && !nxt[p][c]) {
    nxt[p][c] = np;
    p = par[p];
  }
  if (!p)
    par[np] = rt;
  else {
    int q = nxt[p][c];
    if (len[p] + 1 == len[q])
      par[np] = q;
    else {
      int nq = newNode(len[p] + 1);
      memcpy(nxt[nq], nxt[q], sizeof nxt[q]);
      par[nq] = par[q];
      par[q] = par[np] = nq;
      while (p && nxt[p][c] == q) {
        nxt[p][c] = nq;
        p = par[p];
      }
    }
  }
  last = np;
}
void ins(char s[]) {
  for (int i = 0; s[i]; i++) {
    add(s[i] - 'a');
  }
}
long long cal(char s[]) {
  for (int i = 0; i <= tol; i++) cur[i] = 0;
  for (int i = 1; i <= tol; i++) cur[len[i]]++;
  for (int i = 1; i <= tol; i++) cur[i] += cur[i - 1];
  for (int i = 1; i <= tol; i++) pos[cur[len[i]]--] = i;
  for (int i = 0, p = rt; s[i]; i++) {
    g[p = nxt[p][s[i] - 'a']]++;
  }
  for (int i = tol; i >= 1; i--) {
    int u = pos[i];
    g[par[u]] += g[u];
  }
  long long ans = 0;
  for (int i = 2; i <= tol; i++) {
    ans += (long long)(len[i] - len[par[i]]) * g[i] * (g[i] + 1) / 2;
  }
  return ans;
}
}  // namespace SAM
char str[maxn];
int main() {
  using namespace SAM;
  scanf("%s", str);
  init();
  ins(str);
  cout << cal(str) << '\n';
  return 0;
}