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 = 110000;
const int MAXS = 256;
int n;
char a[MAXN];
int sa[MAXN], rnk[2 * MAXN], rnk1[2 * MAXN];
int st[MAXS], cnt[MAXN], tmp[MAXN];
int height[MAXN], top;
struct Node {
  int id, val;
  Node(int i = 0, int v = 0) : id(i), val(v) {}
} sta[MAXN];
int main() {
  scanf("%s", a + 1);
  n = strlen(a + 1);
  memset(st, 0, sizeof st);
  memset(rnk, 0, sizeof rnk);
  for (int i = 1; i <= n; i++) st[a[i]] = 1;
  for (int i = 1; i < MAXS; i++) st[i] += st[i - 1];
  for (int i = 1; i <= n; i++) rnk[i] = st[a[i]];
  for (int k = 0, p = 1; k < n && p <= n; p <<= 1) {
    memset(cnt, 0, sizeof cnt);
    for (int i = 1; i <= n; i++) cnt[rnk[i + p]]++;
    for (int i = 1; i <= n; i++) cnt[i] += cnt[i - 1];
    for (int i = n; i >= 1; i--) tmp[cnt[rnk[i + p]]--] = i;
    memset(cnt, 0, sizeof cnt);
    for (int i = 1; i <= n; i++) cnt[rnk[i]]++;
    for (int i = 1; i <= n; i++) cnt[i] += cnt[i - 1];
    for (int i = n; i >= 1; i--) sa[cnt[rnk[tmp[i]]]--] = tmp[i];
    memcpy(rnk1, rnk, sizeof rnk1);
    rnk[sa[1]] = k = 1;
    for (int i = 2; i <= n; i++) {
      if (rnk1[sa[i]] != rnk1[sa[i - 1]] ||
          rnk1[sa[i] + p] != rnk1[sa[i - 1] + p])
        k++;
      rnk[sa[i]] = k;
    }
  }
  height[n + 1] = 0;
  for (int i = 1, k = 0; i <= n; i++) {
    if (rnk[i] == 1) {
      height[rnk[i]] = k = 0;
      continue;
    }
    if (--k < 0) k = 0;
    while (a[i + k] == a[sa[rnk[i] - 1] + k]) k++;
    height[rnk[i]] = k;
  }
  long long ans = 0;
  for (int i = 1; i <= n; i++)
    ans += n - sa[i] + 1 - max(height[i], height[i + 1]);
  top = 0;
  for (int i = 1; i <= n + 1; i++) {
    int t = i;
    while (top > 0 && height[i] < sta[top - 1].val) {
      int l = i - sta[--top].id + 1;
      int k = sta[top].val - max(height[i], top > 0 ? sta[top - 1].val : 0);
      ans += 1ll * l * (l + 1) / 2 * k;
      t = min(t, sta[top].id);
    }
    if (top == 0 || height[i] > sta[top - 1].val)
      sta[top++] = Node(t, height[i]);
  }
  cout << ans << endl;
  return 0;
}