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;
char buf[1 << 15], *fs, *ft;
inline char getc() {
  return (fs == ft &&
          (ft = (fs = buf) + fread(buf, 1, 1 << 15, stdin), fs == ft))
             ? 0
             : *fs++;
}
inline int read() {
  register int x = 0, f = 1;
  register char ch = getc();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getc();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getc();
  }
  return x * f;
}
const int MAXN = 100010 << 1;
int n, m, cnt = 1, last = 1;
char a[MAXN];
struct wy {
  int ch[26];
  int fa, len;
} t[MAXN];
int f[MAXN];
int c[MAXN], s[MAXN];
inline void insert(int x) {
  int p = last;
  int np = last = ++cnt;
  t[np].len = t[p].len + 1;
  while (p && !t[p].ch[x]) {
    t[p].ch[x] = np;
    p = t[p].fa;
  }
  if (!p)
    t[np].fa = 1;
  else {
    int q = t[p].ch[x];
    if (t[q].len == t[p].len + 1)
      t[np].fa = q;
    else {
      int nq = ++cnt;
      t[nq] = t[q];
      t[nq].len = t[p].len + 1;
      t[np].fa = t[q].fa = nq;
      while (p && t[p].ch[x] == q) {
        t[p].ch[x] = nq;
        p = t[p].fa;
      }
    }
  }
}
int main() {
  scanf("%s", a + 1);
  n = strlen(a + 1);
  for (register int i = 1; i <= n; ++i) insert(a[i] - 'a'), ++f[last];
  for (int i = 1; i <= cnt; ++i) ++c[t[i].len];
  for (int i = 1; i <= n; ++i) c[i] += c[i - 1];
  for (int i = 1; i <= cnt; ++i) s[c[t[i].len]--] = i;
  long long ans = 0;
  for (int i = cnt; i >= 1; --i) {
    int x = s[i];
    f[t[x].fa] += f[x];
    ans = (ans + (long long)(t[x].len - t[t[x].fa].len) *
                     ((long long)f[x] * (f[x] + 1) / 2));
  }
  printf("%lld\n", ans);
  return 0;
}