One day, Twilight Sparkle is interested in how to sort a sequence of integers a1, a2, ..., an in non-decreasing order. Being a young unicorn, the only operation she can perform is a unit shift. That is, she can move the last element of the sequence to its beginning:

a1, a2, ..., an → an, a1, a2, ..., an - 1.

Help Twilight Sparkle to calculate: what is the minimum number of operations that she needs to sort the sequence?

Input

The first line contains an integer n (2 ≤ n ≤ 105). The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105).

Output

If it's impossible to sort the sequence output -1. Otherwise output the minimum number of operations Twilight Sparkle needs to sort it.

Examples

Input

2
2 1


Output

1


Input

3
1 3 2


Output

-1


Input

2
1 2


Output

0
# import sys
# sys.stdout = open('output.txt', 'wt')
# sys.stdin = open('input.txt', 'r')
n = int(input())
a = list(map(int, input().split()))
f, c = 1, 1
for i in range(1, n):
    if f:
        if a[i] < a[i-1]:
            f = 0
    else:
        if a[i] < a[i-1]:
            print(-1)
            f = -1
            break
        else:
            c += 1
# if n == 2:
#     print(1)
else:
    if f != -1:
        if f == 1:
            print(0)
        else:
            if a[-1] > a[0]:
                print(-1)
            else:
                print(c)