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=int(input())
l=input().split()
for i in range(n):
    l[i]=int(l[i])
k=l.index(min(l))
if(k==0 and l[-1]==l[k]):
    i=n-1
    while(i>-1 and l[i]==l[k]):
        i-=1
    k=i+1
j=k
i=j+1
s=1
while(s<n):
    if(i==n):
        i=i%n
    if(j==n):
        j=j%n
    if(l[j]<=l[i]):
        s+=1
        j+=1
        i+=1
    else:
        break

if(s==n):
    if(k==0):
        print(0)
    else:
        print(n-k)
else:
    print(-1)
