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
sys.setrecursionlimit(10 ** 7)

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

N = int(input())
A = list(map(int, input().split()))

idx = [0] * (N+1)
for i in range(N):
    a = A[i]
    idx[a] = i


class SegmentTree:
    """
    引数：
        N: 処理する区間の長さ
        operator: モノイド演算 (max, min, __add__,ラムダ式,関数定義など)
        UNIT: 単位元
        a: 長さNの配列 a で初期化（a を与えない場合、単位元で初期化）
    注意: 内部的には 1-indexed
    """

    def __init__(self, N, operator, unit, a=None):
        self.op = operator
        self.UNIT = unit

        self.N0 = 2**(N-1).bit_length()
        self.tree = [self.UNIT]*(2*self.N0)
        if a != None:
            self.tree[self.N0:self.N0+N] = a[:]
            for k in range(self.N0-1, 0, -1):
                self.tree[k] = self.op(self.tree[2*k], self.tree[2*k+1])

    # a_k の値を x に更新
    def update(self, k, x):
        k += self.N0
        self.tree[k] = x
        k //= 2
        while k:
            self.tree[k] = self.op(self.tree[2*k], self.tree[2*k+1])
            k //= 2

    # 区間[l,r)をopでまとめる
    def query(self, l, r):
        L = l + self.N0
        R = r + self.N0
        s = self.UNIT
        while L < R:
            if R & 1:
                R -= 1
                s = self.op(self.tree[R], s)
            if L & 1:
                s = self.op(s, self.tree[L])
                L += 1
            L >>= 1
            R >>= 1
        return s

    def get(self, k):  # k番目の値を取得。query[k,k]と同じ
        return self.tree[k + self.N0]

    def all(self):
        return self.tree[1]


seg_sml = SegmentTree(N, min, N)
seg_big = SegmentTree(N, max, -1)

ans = 0

for a in range(1, N + 1):
    i = idx[a]
    l = seg_big.query(0, i)
    r = seg_sml.query(i, N)

    left = i - l - 1
    right = r - i - 1

    cnt = (r - l - 1) * (r - l) // 2
    cnt -= left * (left + 1) // 2
    cnt -= right * (right + 1) // 2

    ans += cnt * a

    seg_sml.update(i, i)
    seg_big.update(i, i)


print(ans)
