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(input())
v=[int(i) for i in input().split()]
last=-1
first=v[0]
for i in range(len(v)):
    if v[i]<last:
        break
    else:
        last=v[i]
else:
    print(0)
    sys.exit()
pos=i
#print('pos=%d'%pos)
last=-1
for i in range(i,len(v)):
    if v[i]<last or v[i]>first:
        print(-1)
        sys.exit()
    else:
        last=v[i]
print(len(v)-pos)
