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 = raw_input().split()
x = [0] * n
for i in range(0, n):
        x[i] = eval( a[i] )

lef = [1] * n
for i in range(1, n):
        lef[i] = lef[ i - 1] and ( x[i] >= x[i - 1] )

rig = [1] * n
rig[n - 1] = ( x[n - 1] <= x[0] )
for i in range(n - 1, 0, -1):
        rig[i - 1] = rig[i] and ( x[i] >= x[i-1] )

if lef[n - 1]:
        print 0
else:
        ans = n
        for i in range(1, n):
                if lef[i - 1] and rig[i]:
                        ans = n - i
        if ans == n:
                ans = -1
        print ans