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
#!/usr/bin/env python


def read():
    raw_input()
    return map(int, raw_input().split())


def work(vList):
    cnt = 0
    for i in range(len(vList) - 1):
        if vList[i] > vList[i + 1]:
            vList = vList[i + 1:] + vList[:i + 1]
            cnt = len(vList) - i - 1
            break

    if cnt == 0:
        print 0
        return
    
    for i in range(len(vList) - 1):
        if vList[i] > vList[i + 1]:
            print -1
            return
    
    print cnt


if __name__ == "__main__":
    work(read())
