One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

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Constraints

* 1 ≦ N ≦ 200,000
* (a_1, a_2, ..., a_N) is a permutation of (1, 2, ..., N).

Input

The input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print the answer.

Note that the answer may not fit into a 32-bit integer.

Examples

Input

3
2 1 3


Output

9


Input

4
1 3 2 4


Output

19


Input

8
5 4 8 1 2 6 7 3


Output

85
#include <stdio.h>
#include <set>
typedef long long ll;

int main(void) {
  ll i, n, ans = 0;
  scanf("%lld", &n);
  ll a, pos[n];
  for(i = 0; i < n; ++i) {
    scanf("%lld", &a);
    pos[--a] = i;
  }
  std::set<ll> s;
  std::set<ll>::iterator it;
  for(i = 0; i < n; ++i) {
    ll x = pos[i] + 1, y = n - pos[i];
    it = s.lower_bound(pos[i]);
    if(it != s.end()) y = (*it) - pos[i];
    if(it != s.begin()) x = pos[i] - *(--it);
    ans += x * y * (i + 1);
    s.insert(pos[i]);
  }
  printf("%lld", ans);
  return 0;
}