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 <bits/stdc++.h>
using namespace std;
typedef long long LL;
int a[200005], pos[200005];
set<int> st;
set<int>::iterator its;
int main(){
	int n;
	scanf("%d", &n);
	for(int i=1;i<=n;i++){
		scanf("%d", &a[i]);
		pos[a[i]] = i;
	}
	LL ans = 0;
	for(int i=1;i<=n;i++){
		int l = 1, r = n;
		int p = pos[i];
		its = st.lower_bound(p);
		if(its != st.end()) r = *its-1;
		if(its != st.begin()) its--, l = *its+1;
		int le = p-l+1, re = r-p+1;
		ans += (LL)re*le*i;
		st.insert(p);
	}
	printf("%lld\n", ans);
}