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(raw_input())
#out = sys.stdout.write
a = map(int,raw_input().split())
brk = 0
cnt = 0
for i in xrange(1,n):
    if brk>=1:
        cnt+=1
    if a[i-1] > a[i]:
        brk+=1
        cnt+=1
if a[n-1] > a[0]:
    brk+=1 

if brk <= 1:
    print cnt
else:
    print -1
