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 ll = long long;
constexpr ll inf = static_cast<ll>(1e15);
constexpr ll mod = static_cast<ll>(1e9 + 7);

int n;
ll a[200005];
int main()
{
	std::cin >> n;
	for (int i = 1; i <= n; ++i) {
		ll tmp;
		std::cin >> tmp;
		a[tmp] = i;
	}

	std::set<ll> st{ 0,n + 1 };
	ll ans = 0;
	for (int i = 1; i <= n; ++i)
	{
		auto p = st.upper_bound(a[i]);
		auto r = *p;
		auto l = *(--p);
		ans += i * (r - a[i])*(a[i] - l);
		st.insert(a[i]);
	}

	std::cout << ans << std::endl;
	return 0;
}
