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 MAXLEN = 101000;
const int K = 26;
struct state {
  int length, link;
  int next[K];
  bool clonned;
};
state st[MAXLEN * 2 - 1];
int sz, last;
void init() {
  st[0].link = -1;
  memset(st[0].next, -1, sizeof st[0].next);
  ++sz;
}
void sa_extend(char c) {
  c -= 'a';
  int nlast = sz++;
  st[nlast].length = st[last].length + 1;
  memset(st[nlast].next, -1, sizeof st[nlast].next);
  int p;
  for (p = last; p != -1 && st[p].next[c] == -1; p = st[p].link)
    st[p].next[c] = nlast;
  if (p == -1)
    st[nlast].link = 0;
  else {
    int q = st[p].next[c];
    if (st[p].length + 1 == st[q].length)
      st[nlast].link = q;
    else {
      int clone = sz++;
      st[clone].length = st[p].length + 1;
      memcpy(st[clone].next, st[q].next, sizeof st[clone].next);
      st[clone].link = st[q].link;
      for (; p != -1 && st[p].next[c] == q; p = st[p].link)
        st[p].next[c] = clone;
      st[q].link = st[nlast].link = clone;
      st[clone].clonned = 1;
    }
  }
  last = nlast;
}
string s;
vector<int> g[MAXLEN * 2], bg[MAXLEN * 2];
bool u[MAXLEN * 2], used[MAXLEN * 2];
long long dp[MAXLEN * 2], dp2[MAXLEN * 2];
long long go(int v) {
  if (u[v]) return dp[v];
  u[v] = 1;
  dp[v] = !st[v].clonned;
  for (int i = 0; i < (int)g[v].size(); i++) dp[v] += go(g[v][i]);
  return dp[v];
}
long long go2(int v) {
  if (!v) return 1;
  if (used[v]) return dp2[v];
  used[v] = 1;
  for (int i = 0; i < (int)bg[v].size(); i++) dp2[v] += go2(bg[v][i]);
  return dp2[v];
}
int main() {
  cin >> s;
  int n = (int)s.size();
  init();
  for (int i = 0; i < n; i++) sa_extend(s[i]);
  for (int i = 0; i < sz; i++) {
    if (i) g[st[i].link].push_back(i);
    for (int j = 0; j < K; j++)
      if (st[i].next[j] != -1) bg[st[i].next[j]].push_back(i);
  }
  long long ans = 0;
  for (int i = 1; i < sz; i++) {
    long long t = go(i);
    if (t % 2 == 0)
      t = (t / 2) * (t + 1);
    else
      t = ((t + 1) / 2) * t;
    t *= go2(i);
    ans += t;
  }
  cout << ans << endl;
  return 0;
}