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>
const int kN = 1e5 + 10;
int lth;
char s[kN];
inline int read() {
  int f = 1, w = 0;
  char ch = getchar();
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') f = -1;
  for (; isdigit(ch); ch = getchar()) w = (w << 3) + (w << 1) + (ch ^ '0');
  return f * w;
}
void Chkmax(int &fir, int sec) {
  if (sec > fir) fir = sec;
}
void Chkmin(int &fir, int sec) {
  if (sec < fir) fir = sec;
}
namespace SAM {
const int kNode = kN << 1;
int node_num = 1, last = 1;
int link[kNode], len[kNode], sz[kNode], tr[kNode][26];
int id[kNode], cnt[kN];
void Insert(int ch_) {
  int p = last, now_ = last = ++node_num;
  sz[now_] = 1, len[now_] = len[p] + 1;
  for (; p && !tr[p][ch_]; p = link[p]) tr[p][ch_] = now_;
  if (!p) {
    link[now_] = 1;
    return;
  }
  int q = tr[p][ch_];
  if (len[q] == len[p] + 1) {
    link[now_] = q;
    return;
  }
  int newq = ++node_num;
  len[newq] = len[p] + 1;
  link[newq] = link[q];
  link[q] = link[now_] = newq;
  memcpy(tr[newq], tr[q], sizeof(tr[q]));
  for (; p && tr[p][ch_] == q; p = link[p]) tr[p][ch_] = newq;
}
long long Query() {
  for (int i = 1; i <= node_num; ++i) ++cnt[len[i]];
  for (int i = 1; i <= lth; ++i) cnt[i] += cnt[i - 1];
  for (int i = node_num; i >= 1; --i) id[--cnt[len[i]]] = i;
  long long ans = 0;
  for (int i = node_num; i >= 1; --i) {
    sz[link[id[i]]] += sz[id[i]];
    ans += 1ll * sz[id[i]] * (sz[id[i]] + 1) / 2ll *
           (len[id[i]] - len[link[id[i]]]);
  }
  return ans;
}
}  // namespace SAM
int main() {
  scanf("%s", s + 1);
  lth = strlen(s + 1);
  for (int i = 1; i <= lth; ++i) SAM::Insert(s[i] - 'a');
  printf("%lld\n", SAM::Query());
  return 0;
}