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
n = int(input())
a = list(map(int, input().split()))
index = [[] for _ in range(n+1)]
for i in range(n):
	index[a[i]] = i

l = list(range(n))
r = list(range(n))

ans = 0
for i in range(n, 0, -1):
	m = index[i]
	ans += i * (r[m] - m + 1) * (m - l[m] + 1)
	if l[m] > 0:
		r[l[m] - 1] = r[m]
	if r[m] < n-1:
		l[r[m] + 1] = l[m]

print(ans)