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/pypy3

from sys import stdin,stderr

def readInts(): return map(int,stdin.readline().strip().split())
def print_err(*args,**kwargs): print(*args,file=stderr,**kwargs)
    
def solve(n,ns):
    v = ns[0]
    v0 = v
    inversions = 0
    iix = n
    for ix in range(1,n):
        v2 = ns[ix]
        if v2<v:
            inversions += 1
            iix = ix
        if inversions > 1: return -1
        if inversions and v2 > v0: return -1
        v = v2
    return n-iix

def run():
    n, = readInts()
    ns = list(readInts())
    print(solve(n,ns))
        
run()
