One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

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をソート
b = [0] * N
for i in range(N):
    b[a[i] - 1] = i

# 初期化　端っこ対策としてひとつ余計に取っている
left = [0] * (N + 1)
right = [0] * (N + 1)
for i in range(N + 1):
    left[i] = i-1
    right[i] = i+1

# 更新
for idx in reversed(b):
    left[right[idx]] = left[idx]
    right[left[idx]] = right[idx]

ans = 0
for i in range(N):
    ans += a[i] * (i - left[i]) * (right[i] - i)

print(ans)