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;

ll n, a[200005], cur, ans;
vector<ll> st;

int main()
{
	scanf("%lld",&n);
	for(ll i=1;i<=n;i++) {
		scanf("%lld",&a[i]);
	}
	st.push_back(0);
	for(ll i=1;i<=n;i++) {
		while(!st.empty()) {
			if(a[st.back()] >= a[i]) {
				ll T = st.back(); st.pop_back();
				cur -= (T - st.back()) * a[T];
			}
			else break;
		}
		cur += (i - st.back()) * a[i];
		st.push_back(i);
		ans += cur;
	}
	printf("%lld\n",ans);
}
