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 MAXN = 100005;
template <typename T>
void chkmax(T &x, T y) {
  x = max(x, y);
}
template <typename T>
void chkmin(T &x, T y) {
  x = min(x, y);
}
template <typename T>
void read(T &x) {
  x = 0;
  int f = 1;
  char c = getchar();
  for (; !isdigit(c); c = getchar())
    if (c == '-') f = -f;
  for (; isdigit(c); c = getchar()) x = x * 10 + c - '0';
  x *= f;
}
template <typename T>
void write(T x) {
  if (x < 0) x = -x, putchar('-');
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
}
template <typename T>
void writeln(T x) {
  write(x);
  puts("");
}
namespace SuffixAutomaton {
const int MAXN = 2 * 100005;
const int MAXC = 26;
int root, size, last;
int child[MAXN][MAXC];
int fail[MAXN], depth[MAXN], cnt[MAXN];
vector<int> a[MAXN];
long long ans;
int newnode(int dep) {
  fail[size] = 0;
  depth[size] = dep;
  memset(child[size], 0, sizeof(child[size]));
  return size++;
}
void extend(int ch) {
  int p = last, np = newnode(depth[last] + 1);
  while (child[p][ch] == 0) {
    child[p][ch] = np;
    p = fail[p];
  }
  if (child[p][ch] == np)
    fail[np] = root;
  else {
    int q = child[p][ch];
    if (depth[q] == depth[p] + 1)
      fail[np] = q;
    else {
      int nq = newnode(depth[p] + 1);
      fail[nq] = fail[q];
      fail[q] = fail[np] = nq;
      memcpy(child[nq], child[q], sizeof(child[q]));
      while (child[p][ch] == q) {
        child[p][ch] = nq;
        p = fail[p];
      }
    }
  }
  cnt[last = np]++;
}
void init(char *s) {
  size = 0;
  root = last = newnode(0);
  int len = strlen(s + 1);
  for (int i = 1; i <= len; i++) extend(s[i] - 'a');
}
long long f(long long x) { return x * (x + 1) / 2; }
void work(int pos) {
  for (unsigned i = 0; i < a[pos].size(); i++) {
    work(a[pos][i]);
    cnt[pos] += cnt[a[pos][i]];
  }
  ans += f(cnt[pos]) * (depth[pos] - depth[fail[pos]]);
}
void calc() {
  for (int i = 1; i < size; i++) a[fail[i]].push_back(i);
  work(0);
  writeln(ans);
}
}  // namespace SuffixAutomaton
char s[MAXN];
int main() {
  scanf("%s", s + 1);
  SuffixAutomaton::init(s);
  SuffixAutomaton::calc();
  return 0;
}