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 MaxN = 2e5 + 50;
template <class t>
inline void read(t &s) {
  s = 0;
  register int f = 1;
  register char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) s = (s << 3) + (s << 1) + (c ^ 48), c = getchar();
  s *= f;
  return;
}
template <class t, class... A>
inline void read(t &x, A &...a) {
  read(x);
  read(a...);
}
template <class t>
inline void write(t x) {
  if (x < 0) putchar('-'), x = -x;
  int buf[21], top = 0;
  while (x) buf[++top] = x % 10, x /= 10;
  if (!top) buf[++top] = 0;
  while (top) putchar(buf[top--] ^ '0');
  return;
}
inline void setIn(std::string s) {
  freopen(s.c_str(), "r", stdin);
  return;
}
inline void setOut(std::string s) {
  freopen(s.c_str(), "w", stdout);
  return;
}
inline void setIO(std::string s = "") {
  setIn(s + ".in");
  setOut(s + ".out");
  return;
}
template <class t>
inline bool checkmin(t &x, t y) {
  if (x > y) {
    x = y;
    return 1;
  }
  return 0;
}
template <class t>
inline bool checkmax(t &x, t y) {
  if (x < y) {
    x = y;
    return 1;
  }
  return 0;
}
inline int lowbit(int x) { return x & (-x); }
int ch[MaxN][26], fa[MaxN], len[MaxN], ndn = 1, cur = 1;
char s[MaxN];
std::vector<int> E[MaxN];
long long cnt[MaxN], ans;
inline void extend(int c) {
  int lst = cur;
  len[cur = ++ndn] = len[lst] + 1, cnt[ndn] = 1;
  register int p = lst;
  for (; p && !ch[p][c]; ch[p][c] = cur, p = fa[p])
    ;
  if (!p) return fa[cur] = 1, void();
  register int q = ch[p][c];
  if (len[q] == len[p] + 1) return fa[cur] = q, void();
  register int clone = ++ndn;
  std::memcpy(ch[clone], ch[q], sizeof(ch[q]));
  len[clone] = len[p] + 1, fa[clone] = fa[q], fa[q] = fa[cur] = clone;
  for (; p && ch[p][c] == q; ch[p][c] = clone, p = fa[p])
    ;
}
inline void dfs(int u, int fa) {
  for (auto v : E[u]) dfs(v, u), cnt[u] += cnt[v];
  ans += cnt[u] * (cnt[u] + 1) / 2 * (len[u] - len[fa]);
}
signed main(void) {
  int n;
  std::scanf("%s", s + 1), n = std::strlen(s + 1);
  for (int i = 1; i <= n; ++i) extend(s[i] - 'a');
  for (int i = 1; i <= ndn; ++i) E[fa[i]].push_back(i);
  dfs(1, 0);
  write(ans), std::puts("");
  return 0;
}