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 N = 4e5 + 11;
namespace SAM {
char S[N];
long long ans = 0;
int ch[N][27], fa[N], l[N], sz[N];
int las = 1, cnt = 1, n, q;
vector<int> to[N];
inline void extend(int c) {
  int p = las, np = ++cnt;
  las = cnt, l[np] = l[p] + 1, sz[np] = 1;
  for (; p && !ch[p][c]; p = fa[p]) ch[p][c] = np;
  if (!p)
    fa[np] = 1;
  else {
    int q = ch[p][c];
    if (l[q] == l[p] + 1)
      fa[np] = q;
    else {
      int nq = ++cnt;
      l[nq] = l[p] + 1;
      memcpy(ch[nq], ch[q], sizeof ch[q]);
      fa[nq] = fa[q], fa[q] = fa[np] = nq;
      for (; p && ch[p][c] == q; p = fa[p]) ch[p][c] = nq;
    }
  }
}
inline void dfs(int x) {
  for (auto v : to[x]) {
    dfs(v);
    sz[x] += sz[v];
  }
  ans += 1ll * sz[x] * (sz[x] + 1) / 2 * (l[x] - l[fa[x]]);
}
inline void main() {
  ans = 0;
  las = 1, cnt = 1;
  scanf("%s", S + 1);
  n = strlen(S + 1);
  for (register int i = 1; i <= n; ++i) extend(S[i] - 'a');
  for (register int i = 2; i <= cnt; ++i) to[fa[i]].push_back(i);
  dfs(1);
  printf("%lld\n", ans);
  for (register int i = 1; i <= cnt; ++i)
    to[i].clear(), memset(ch[i], 0, sizeof ch[i]), sz[i] = l[i] = fa[i] = 0;
}
}  // namespace SAM
int main() {
  SAM::main();
  return 0;
}