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 Max_n = 1e5 + 5;
int n, M;
long long ans;
int sa[Max_n], rk[Max_n], tp[Max_n], ht[Max_n], buk[Max_n];
int top;
char s[Max_n];
void Bsort() {
  for (int i = 1; i <= M; i++) buk[i] = 0;
  for (int i = 1; i <= n; i++) buk[rk[i]]++;
  for (int i = 1; i <= M; i++) buk[i] += buk[i - 1];
  for (int i = n; i >= 1; i--) sa[buk[rk[tp[i]]]--] = tp[i];
}
struct node {
  int x, v;
} stk[Max_n];
int main() {
  scanf("%s", s + 1);
  n = strlen(s + 1);
  M = 26;
  for (int i = 1; i <= n; i++) rk[i] = s[i] - 'a' + 1, tp[i] = i;
  Bsort();
  for (int len = 1, cnt = 0; cnt < n; M = cnt, len <<= 1) {
    cnt = 0;
    for (int i = n - len + 1; i <= n; i++) tp[++cnt] = i;
    for (int i = 1; i <= n; i++)
      if (sa[i] > len) tp[++cnt] = sa[i] - len;
    Bsort();
    swap(tp, rk);
    rk[sa[1]] = cnt = 1;
    for (int i = 2; i <= n; i++) {
      if (tp[sa[i]] != tp[sa[i - 1]] || tp[sa[i] + len] != tp[sa[i - 1] + len])
        cnt++;
      rk[sa[i]] = cnt;
    }
  }
  for (int i = 1, len = 0; i <= n; i++) {
    if (len) len--;
    while (s[sa[rk[i] - 1] + len] == s[i + len]) len++;
    ht[rk[i]] = len;
  }
  for (int i = 1; i <= n; i++) ans += n - sa[i] + 1 - max(ht[i], ht[i + 1]);
  for (int i = 1; i <= n + 1; i++) {
    int now = i;
    while (top && ht[i] < stk[top].v) {
      int len = i - stk[top].x + 1;
      int num = stk[top].v - max(ht[i], top > 1 ? stk[top - 1].v : 0);
      ans += 1ll * len * (len + 1) / 2 * num;
      now = min(now, stk[top--].x);
    }
    stk[++top] = (node){now, ht[i]};
  }
  cout << ans;
}