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())
sl=list(map(int,input().split()))
p=max(sl)
q=min(sl)
a=-1
k=0
pp=10000000000
for i in range(1,n):
    if sl[i]>=sl[i-1]:
        if a<0:
            pp=min(pp,sl[i-1])
        if a>=0:
            k=max(k,sl[i])
        continue
    else:
        if (p==sl[i-1] and q==sl[i]) :
            a+=1
            ans=n-i 
        else:
            a=-2
            break
if k>pp:
    a=-2
if a==-1:
    print("0")
elif a==-2 or a>0:
    print("-1")
elif a==0:
    print(ans)