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
n = int(sys.stdin.readline())


I = -1
l = map(int, sys.stdin.readline().split())
for i in range(0,n):
    if(l[i-1]>l[i]):
        if(I == -1):
            I = i
            continue
        else:
            I = -2
            break
    else:
        continue

if(I == -2):
    print -1
elif(I == -1):
    print 0
else:
    I = (n-I)%n
    print I