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(raw_input())
a=map(int,raw_input().split())
so=sorted(a)
t=0
for i in range(1,len(a)):
    if a[i]>=a[t]:
        t=i
    else:
        break
#print n-t-1
t=t+1
#print a[:t]
r=a[t:]
#print r
#r.reverse()
#print r
b=r+a[:t]
#print b
#print so
if b!=so:
    print "-1"
else:
    print n-t
    

##n=int(raw_input())
##b=[]
##for i in range(n):
##    b.append('')
##for i in range(n/2+1):
##    #for j in range(2*i+1):
##    b[i]='*'*((n-(2*i+1))/2)+'D'*(2*i+1)+'*'*((n-(2*i+1))/2)
##    b[n-i-1]=b[i]
##for i in b:    
##    print i
