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 SIZE = 100005;
int gap, tmp[SIZE * 2];
class SuffixArray {
 public:
  int sa[SIZE], rk[SIZE], ht[SIZE];
  static bool cmp(int x, int y) {
    if (tmp[x] != tmp[y]) return tmp[x] < tmp[y];
    return tmp[x + gap] < tmp[y + gap];
  }
  void gao(const char* s, int n) {
    copy(s, s + n + 1, rk);
    for (gap = 1; gap <= n; gap <<= 1) {
      for (int i = 0; i <= n; i++) sa[i] = i;
      copy(rk, rk + n + 1, tmp);
      sort(sa, sa + n + 1, cmp);
      for (int i = rk[*sa] = 0; i < n; i++)
        rk[sa[i + 1]] = rk[sa[i]] + cmp(sa[i], sa[i + 1]);
    }
    for (int i = gap = ht[*sa] = 0; i < n; i++) {
      if (gap) --gap;
      while (s[i + gap] == s[sa[rk[i] - 1] + gap]) gap++;
      ht[rk[i]] = gap;
    }
  }
};
char str[SIZE];
SuffixArray SA;
int main() {
  int n = strlen(gets(str));
  long long ans = n * (n + 1ll) / 2, cnt = 0;
  SA.gao(str, n);
  vector<int> u = {0};
  for (int i = 1; i <= n; i++) {
    while (SA.ht[i] < SA.ht[u.back()]) {
      cnt -= SA.ht[u.back()] * (u.back() - u[u.size() - 2]);
      u.pop_back();
    }
    u.push_back(i);
    cnt += SA.ht[u.back()] * (u.back() - u[u.size() - 2]);
    ans += cnt;
  }
  printf("%I64d\n", ans);
}