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
def main():
    n=input()
    m=map(int,raw_input().split())
    start=1
    k=m[:]
    k.sort()
    if k==m:
        print 0
        return
    
    while m[start]>=m[start-1]:
        start+=1
    end=start+1
    while end<n and m[end]>=m[end-1]:
        end+=1
    if end==n and m[0]>=m[-1]:
        print n-start 
        return
    print -1
main()
