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 = tuple(map(int,input().split()))

left_amin = [0]*N

stack = [(0,-1)]

for i,a in enumerate(A):
    while stack[-1][0] > a:
        stack.pop()
    left_amin[i] = stack[-1][1]
    stack.append((a,i))

right_amin = [0]*N

stack = [(0,N)]

for i,a in zip(reversed(range(N)),reversed(A)):
    while stack[-1][0] > a:
        stack.pop()
    right_amin[i] = stack[-1][1]
    stack.append((a,i))


res = 0

for i,(l,r,a) in enumerate(zip(left_amin,right_amin,A)):
    res += a*(i-l)*(r-i)
print(res)