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
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)

n, *a = map(int, read().split())
ans = 0
l = list(range(n + 1))
r = list(range(n + 1))
memo = [0] * (n + 1)
for i, aa in enumerate(a):
    memo[aa] = i
for i in range(n, -1, -1):
    v = memo[i]
    ans += (v - l[v] + 1) * (r[v] - v + 1) * i
    l[r[v] + 1], r[l[v] - 1] = l[v], r[v]
print(ans)
