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
def naek(a,indeks):
    for x in range(indeks,len(a)-1):
        if a[x]>a[x+1]:
            return False
            pass
        pass
        pass
    return True
    pass

a=int(input())
a=list(map(int,input().split(" ")))
sor=True
for x in range(len(a)-1):
    if a[x]>a[x+1]:
        sor=False
        idx=x+1
        break
        pass
    pass

if sor:
    print (0)
else:
    if naek(a,idx):
        if a[len(a)-1] > a[0]:
            print (-1)
        else:
            print (len(a)-idx)
            pass
        pass
    else:
        print (-1)        
    pass