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<algorithm>
#include<set>
using namespace std;
int n, w[201000], p[201000];
set<int>Set;
long long res;
int main(){
    int i, a ,b;
    scanf("%d",&n);
    for(i=1;i<=n;i++){
        scanf("%d",&w[i]);
        p[w[i]] = i;
    }
    Set.insert(0);
    Set.insert(n+1);
    for(i=1;i<=n;i++){
        set<int>::iterator it;
        it = Set.lower_bound(p[i]);
        b = *it;
        it--;
        a = *it;
        res += 1ll * (p[i]-a)*(b-p[i])*i;
        Set.insert(p[i]);
    }
    printf("%lld\n",res);
}