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
from collections import deque
n = int(input())
l = [int(x) for x in input().split()]
flag = 0
index = -1
for i in range(len(l) - 1):
    if l[i + 1] < l[i]:
        index = i + 1
        break
if index == -1:
    print(0)
elif index == len(l) - 1:
    if l[index] <= l[0]:
        print(1)
    else:
        print(-1)
else:
    count = 0
    for i in range(index, len(l) - 1):
        if l[i + 1] >= l[i] and l[i] <= l[0] and l[len(l) - 1] <= l[0]:
            count += 1
        else:
            flag = 1
            break
    if flag == 0:
        print(count + 1)
    else:
        print(-1)
