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
n = input()
a = map(int, raw_input().split())
ok = False
x = 10**6
index = -1

for ii in range(1, len(a)):
    if a[ii]<a[ii-1]:
        index = ii
        break
if index+1:
    for ii in range(index+1, len(a)):
        if a[ii]<a[ii-1]:
            ok = True
if ok==True: print '-1'
elif index==-1: print '0'
elif a[-1]>a[0]: print '-1'
else: print n-index
