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 LEN = 1e5 + 5;
const int MAXS = 2 * LEN;
const int K = 26;
int go[MAXS][K];
int slink[MAXS];
int length[MAXS];
bool final[MAXS];
int p, q, size = 1, last = 1, n;
int root = 1;
string s, t;
void extend(int c) {
  for (p = last; !go[p][c]; p = slink[p]) go[p][c] = size;
  q = go[p][c];
  length[size] = length[last] + 1;
  last = size++;
  if (!p)
    slink[last] = 1;
  else if (length[p] + 1 == length[q])
    slink[last] = q;
  else {
    for (length[size] = length[p] + 1; go[p][c] == q; p = slink[p])
      go[p][c] = size;
    memcpy(go[size], go[q], sizeof go[size]);
    slink[size] = slink[q];
    slink[last] = slink[q] = size++;
  }
}
void build() {
  fill(go[root], go[root] + K, 0);
  length[root] = 0;
  size++;
  for (int i = 0; i < (int)s.length(); ++i) extend(s[i] - 'a');
  for (; last > 0; last = slink[last]) final[last] = 1;
}
long long dp1[MAXS];
long long dp2[MAXS];
vector<int> topsort[LEN];
int main() {
  cin >> s;
  build();
  for (int i = 1; i < size; ++i) dp1[i] = LEN;
  for (int i = 0; i < size; ++i) topsort[length[i]].push_back(i);
  for (int vs = 0; vs < LEN; ++vs) {
    for (int i = 0; i < topsort[vs].size(); ++i) {
      int st = topsort[vs][i];
      for (int c = 0; c < 26; ++c) {
        int nxt = go[st][c];
        if (nxt) dp1[nxt] = min(dp1[nxt], dp1[st] + 1);
      }
    }
  }
  for (int vs = LEN - 1; vs > 0; --vs) {
    for (int i = 0; i < topsort[vs].size(); ++i) {
      int st = topsort[vs][i];
      if (final[st]) dp2[st] = 1;
      for (int c = 0; c < 26; ++c) {
        int nxt = go[st][c];
        if (nxt) dp2[st] += dp2[nxt];
      }
    }
  }
  long long ans = 0;
  for (int i = 1; i < size; ++i) {
    long long fx = dp2[i] * (dp2[i] + 1) / 2;
    ans += (length[i] - dp1[i] + 1) * fx;
  }
  cout << ans << endl;
  return 0;
}