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 = 200000 + 10;
char str[maxn];
int r[maxn], len;
struct suffixautomaton {
  int ch[maxn][30], pre[maxn], val[maxn], num[maxn], top[maxn];
  int c[maxn];
  bool vis[maxn];
  int sz, last, cnt;
  void init() {
    pre[0] = -1;
    last = cnt = 0;
    sz = 1;
    memset(vis, 0, sizeof(vis));
    memset(num, 0, sizeof(num));
  }
  void insert(int x) {
    int p = last, np = sz++;
    last = np;
    memset(ch[np], 0, sizeof(ch[np]));
    val[np] = val[p] + 1;
    while (p != -1 && ch[p][x] == 0) {
      ch[p][x] = np;
      p = pre[p];
    }
    if (p == -1)
      pre[np] = 0;
    else {
      int q = ch[p][x];
      if (val[q] == val[p] + 1)
        pre[np] = q;
      else {
        int nq = sz++;
        memcpy(ch[nq], ch[q], sizeof(ch[q]));
        val[nq] = val[p] + 1;
        pre[nq] = pre[q];
        pre[q] = pre[np] = nq;
        while (p != -1 && ch[p][x] == q) {
          ch[p][x] = nq;
          p = pre[p];
        }
      }
    }
  }
  long long slove() {
    memset(c, 0, sizeof(c));
    for (int i = 0; i < sz; ++i) c[val[i]] += 1;
    for (int i = 1; i <= len; ++i) c[i] += c[i - 1];
    for (int i = 0; i < sz; ++i) {
      top[--c[val[i]]] = i;
    }
    for (int i = 0;; i = ch[i][r[val[i]]]) {
      num[i] = 1;
      if (val[i] == len) break;
    }
    for (int i = sz - 1; i > 0; --i) {
      num[pre[top[i]]] += num[top[i]];
    }
    long long res = 0;
    for (int i = 1; i < sz; ++i) {
      res += (num[i] * 1LL * (num[i] + 1) / 2) * (val[i] - val[pre[i]]);
    }
    return res;
  }
} sam;
int main() {
  cin >> str;
  len = strlen(str);
  sam.init();
  for (int i = 0; i < len; ++i) {
    r[i] = str[i] - 'a';
    sam.insert(r[i]);
  }
  cout << sam.slove() << "\n";
  return 0;
}