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 math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time

sys.setrecursionlimit(10**7)
inf = 10**10
mod = 10**9 + 7

def f():
    n = int(input())
    a = list(map(int, input().split()))
    l = list(range(n+2))
    r = list(range(n+2))
    b = [0]*(n+2)
    for i, x in enumerate(a, 1):
        b[x] = i
    c = 0
    for i in range(n,0,-1):
        bi = b[i]
        c += i * (r[bi] - bi + 1) * (bi - l[bi] + 1)
        r[l[bi]-1] = r[bi]
        l[r[bi]+1] = l[bi]
    return c

print(f())
