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>
#define mod 1000000007
#define pb push_back
#define ll long long
using namespace std;
ll place[214514];
int main(){
	ll n,res=0;
	cin>>n;
	vector<ll> a;
	set<ll> used;
	for(ll i=1;i<=n;i++){
		ll x;
		cin>>x;
		a.pb(x);
		place[x]=i;
	}
	used.insert(0);
	used.insert(n+1);
	for(ll i=1;i<=n;i++){
		ll cur = place[i];
		set<ll>::iterator it =  used.upper_bound(cur);
		ll rig = *it;
		it--;
		ll lef = *it;
		res += i * (rig-cur) * (cur-lef);
		used.insert(cur);
	}
	cout<<res<<endl;
	return 0;
}