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/python2
# -*- coding: utf-8 -*-

import sys
import os

def main():
    sys.stdin.readline()
    a = map(int, sys.stdin.readline().split())
    k = -1
    for i in xrange(len(a)-1):
        if a[i] > a[i+1]:
            k = i + 1
            break
    if k < 0:
        print "0"
        return
    a = a[k:] + a[:k]
    ret = len(a) - k

    for i in xrange(len(a)-1):
        if a[i] > a[i+1]:
            ret = -1
            break

    print ret

if __name__ == '__main__':
    main()
