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/python

from collections import deque

def ir():
    return int(raw_input())

def ia():
    line = raw_input()
    line = line.split()
    return map(int, line)

n = ir()
a = ia()


def solve(a):
    a.reverse()
    a = [-e for e in a]
    
    mi, ma = min(a), max(a)
    if ma == mi: print 0; return
    for sp in range(n):
        p = sp - 1
        if p<0: p += n
        if a[p]>a[sp]: break

    for i in range(n-1):
        i = i + sp
        if i>=n: i -= n
        
        j = i +  1
        if j>=n: j -= n
        
        if a[j]<a[i]: print -1; break
    else:
        print sp
        
solve(a)
