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 = [int(i) for i in input().split()]
b = [0]*(n+1)
l = [i for i in range(n+2)]
r = [i for i in range(n+2)]
ans = 0
for i in range(n): b[a[i]]=i
for i in range(n,0,-1):
	m = b[i]
	x,y = l[m],r[m]
	ans+=i*(m-x+1)*(y-m+1)
	l[y+1],r[x-1] = x,y
print(ans)