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
import math

n = int(sys.stdin.readline())
an = [int(x) for x in (sys.stdin.readline()).split()]

t = 0
for i in range(n - 1):
    if(an[i] > an[i + 1]):
        t = i + 1
        break

if(t == 0):
    print(0)
    exit()
       
k = an[0]
v = 0

for i in range(n - 1, t - 1, -1):
    if(an[i] <= k):
        v += 1
        k = an[i]
    else:
        print(-1)
        exit()
        
print(v)