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;
using ll = int64_t;
int main(){
	ll n; cin >> n;
	ll po[n];
	set<ll> hidari, migi;
	hidari.insert(1);
	migi.insert(n);
	for(ll i = 0; i < n; ++i){
		ll a; cin >> a;
		po[--a] = i;
		hidari.insert(-i);
		migi.insert(i);
	}
	ll ans = 0;
	for(ll i = n - 1; i >= 0; --i){
		ll si = -(*hidari.upper_bound(-po[i]));
		ll na = *migi.upper_bound(po[i]);
		hidari.erase(-po[i]);
		migi.erase(po[i]);
		ans += (i + 1) * (po[i] - si) * (na - po[i]);
	}
	cout << ans << endl;
	return 0;
}