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 maxn = 100100;
struct SuffixArray {
  int s[maxn];
  int sa[maxn];
  int rk[maxn];
  int height[maxn];
  int t[maxn], t2[maxn], c[maxn];
  int n;
  void clear() { n = 0; }
  void build_sa(int m) {
    int i, *x = t, *y = t2;
    for (i = 0; i < m; i++) c[i] = 0;
    for (i = 0; i < n; i++) c[x[i] = s[i]]++;
    for (i = 1; i < m; i++) c[i] += c[i - 1];
    for (i = n - 1; i >= 0; i--) sa[--c[x[i]]] = i;
    for (int k = 1; k <= n; k <<= 1) {
      int p = 0;
      for (i = n - k; i < n; i++) y[p++] = i;
      for (i = 0; i < n; i++)
        if (sa[i] >= k) y[p++] = sa[i] - k;
      for (i = 0; i < m; i++) c[i] = 0;
      for (i = 0; i < n; i++) c[x[y[i]]]++;
      for (i = 0; i < m; i++) c[i] += c[i - 1];
      for (i = n - 1; i >= 0; i--) sa[--c[x[y[i]]]] = y[i];
      swap(x, y);
      p = 1;
      x[sa[0]] = 0;
      for (i = 1; i < n; i++)
        x[sa[i]] = y[sa[i - 1]] == y[sa[i]] && y[sa[i - 1] + k] == y[sa[i] + k]
                       ? p - 1
                       : p++;
      if (p >= n) break;
      m = p;
    }
  }
  void build_height() {
    int i, j, k = 0;
    for (i = 0; i < n; i++) rk[sa[i]] = i;
    for (i = 0; i < n - 1; i++) {
      if (k) k--;
      int j = sa[rk[i] - 1];
      while (s[i + k] == s[j + k]) k++;
      height[rk[i]] = k;
    }
  }
  void add(int ch) { s[n++] = ch; }
};
SuffixArray sa;
char s[maxn];
pair<int, int> st[maxn];
int main() {
  scanf("%s", s);
  int len = strlen(s);
  for (int i = 0; s[i]; i++) {
    sa.add(s[i] - 'a' + 1);
  }
  sa.add(0);
  sa.build_sa(27);
  sa.build_height();
  long long ret = 1LL * (len + 1) * len / 2, tmp = 0;
  int tp = 0;
  for (int i = 1; i < sa.n; i++) {
    long long tt = 1;
    while (tp && st[tp].first >= sa.height[i]) {
      tmp -= 1LL * st[tp].first * st[tp].second;
      tt += st[tp--].second;
    }
    tmp += tt * sa.height[i];
    st[++tp] = {sa.height[i], tt};
    ret += tmp;
  }
  cout << ret << endl;
  return 0;
}