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 inf = 0x3fffffff;
const long long mod = 1000000007;
const int maxn = 1e5 + 100;
int sa[maxn];
int t1[maxn], t2[maxn], c[maxn];
int rk[maxn], height[maxn];
void build_sa(int s[], int n, int m) {
  int i, j, p, *x = t1, *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 (j = 1; j <= n; j <<= 1) {
    p = 0;
    for (i = n - j; i < n; i++) y[p++] = i;
    for (i = 0; i < n; i++)
      if (sa[i] >= j) y[p++] = sa[i] - j;
    for (i = 0; i < m; i++) c[i] = 0;
    for (i = 0; i < n; i++) c[x[y[i]]]++;
    for (i = 1; 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] + j] == y[sa[i] + j]
                     ? p - 1
                     : p++;
    if (p >= n) break;
    m = p;
  }
}
void getHeight(int s[], int n) {
  int i, j, k = 0;
  for (i = 0; i <= n; i++) rk[sa[i]] = i;
  for (i = 0; i < n; i++) {
    if (k) k--;
    j = sa[rk[i] - 1];
    while (s[i + k] == s[j + k]) k++;
    height[rk[i]] = k;
  }
}
long long cnt(int x) { return 1ll * x * x; }
char s[maxn];
int a[maxn];
int st[maxn];
vector<pair<pair<int, int>, int>> v;
int main() {
  scanf("%s", s);
  int l = (int)strlen(s);
  for (int i = 0; i < l; i++) a[i] = s[i] - 'a' + 1;
  a[l] = 0;
  build_sa(a, l + 1, 60);
  getHeight(a, l);
  long long ans = 0;
  height[l + 1] = 0;
  sa[l + 1] = l;
  for (int i = 1; i < l + 2; i++) {
    while (!v.empty() && v.back().first.second > height[i]) {
      auto &end = v.back();
      if (end.first.first < height[i]) {
        ans += (end.first.second - height[i]) * cnt(i - end.second);
        end.first.second = height[i];
      } else {
        ans += (end.first.second - end.first.first) * cnt(i - end.second);
        v.pop_back();
      }
    }
    v.push_back({{height[i], l - sa[i]}, i});
  }
  ans += 1ll * l * (l + 1) / 2;
  printf("%lld\n", ans / 2);
  return 0;
}