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;
template <typename T>
inline void read(T &x) {
  x = 0;
  char ch = getchar();
  bool f = false;
  while (!isdigit(ch)) {
    if (ch == '-') {
      f = true;
    }
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = (x << 1) + (x << 3) + (ch ^ 48);
    ch = getchar();
  }
  x = f ? -x : x;
  return;
}
template <typename T>
inline void write(T x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) write(x / 10);
  putchar(x % 10 ^ 48);
  return;
}
const int N = 2e5 + 5;
long long x, n, last = 1, tot = 1, c[N << 1], q[N << 1];
long long Ans;
bool flag;
char str[N];
struct SAM {
  long long son[26];
  long long fa, len, siz;
} t[N << 1];
void Extend(long long c) {
  long long p = last, np = ++tot;
  last = np;
  t[np].len = t[p].len + 1;
  while (p && !t[p].son[c]) t[p].son[c] = np, p = t[p].fa;
  if (!p)
    t[np].fa = 1;
  else {
    long long q = t[p].son[c];
    if (t[p].len + 1 == t[q].len)
      t[np].fa = q;
    else {
      long long nq = ++tot;
      t[nq] = t[q];
      t[nq].len = t[p].len + 1;
      t[nq].siz = 0;
      t[np].fa = t[q].fa = nq;
      while (p && t[p].son[c] == q) t[p].son[c] = nq, p = t[p].fa;
    }
  }
  t[np].siz = 1;
  return;
}
signed main() {
  scanf("%s", str);
  long long len = strlen(str);
  for (long long i = 0; i < len; i++) Extend(str[i] - 'a');
  for (long long i = 1; i <= tot; i++) c[t[i].len]++;
  for (long long i = 1; i <= tot; i++) c[i] += c[i - 1];
  for (long long i = 1; i <= tot; i++) q[c[t[i].len]--] = i;
  for (long long i = tot; i >= 1; i--) t[t[q[i]].fa].siz += t[q[i]].siz;
  for (long long i = tot; i >= 1; i--)
    Ans += 1ll * (t[i].len - t[t[i].fa].len) * (t[i].siz * (t[i].siz + 1)) / 2;
  write(Ans);
  return 0;
}