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

Find the following:

<image>

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<bits/stdc++.h>

#define pb push_back
#define mp make_pair

#define fi first
#define se second

typedef long long ll;
using namespace std;

int a[200500], n;
set<int> s;

int main(){

cin >> n;
for(int i=1;i<=n;i++){
    int x;
    cin >> x;
    a[x] = i;
}
s.insert(0);
s.insert(n + 1);
ll ans = 0;

for(int i=1;i<=n;i++){
    int p = a[i];
    set<int>::iterator it = s.upper_bound(p);
    int r = *it;
    int l = *(--it);
    ans += i * 1ll * (r - p) * 1ll * (p - l);
    s.insert(p);
}
cout << ans;
return 0;
}
