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()))

left = [0] * (N + 1)
right = [0] * (N + 1)

# 左から
buf = list()
for i in range(N):
    while len(buf) > 0 and a[buf[-1]] > a[i]:
        buf.pop()
    if len(buf) > 0:
        left[i] = buf[-1]
    else:
        left[i] = -1
    buf.append(i)

# 右から
buf = list()
for i in reversed(range(N)):
    while len(buf) > 0 and a[buf[-1]] > a[i]:
        buf.pop()
    if len(buf) > 0:
        right[i] = buf[-1]
    else:
        right[i] = N
    buf.append(i)

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

print(ans)