Problem: Artsem has a friend Saunders from University of Chicago. Saunders presented him with the following problem.

Let [n] denote the set {1, ..., n}. We will also write f: [x] → [y] when a function f is defined in integer points 1, ..., x, and all its values are integers from 1 to y.

Now then, you are given a function f: [n] → [n]. Your task is to find a positive integer m, and two functions g: [n] → [m], h: [m] → [n], such that g(h(x)) = x for all <image>, and h(g(x)) = f(x) for all <image>, or determine that finding these is impossible.

Input

The first line contains an integer n (1 ≤ n ≤ 105).

The second line contains n space-separated integers — values f(1), ..., f(n) (1 ≤ f(i) ≤ n).

Output

If there is no answer, print one integer -1.

Otherwise, on the first line print the number m (1 ≤ m ≤ 106). On the second line print n numbers g(1), ..., g(n). On the third line print m numbers h(1), ..., h(m).

If there are several correct answers, you may output any of them. It is guaranteed that if a valid answer exists, then there is an answer satisfying the above restrictions.

Examples

Input

3
1 2 3


Output

3
1 2 3
1 2 3


Input

3
2 2 2


Output

1
1 1 1
2


Input

2
2 1


Output

-1

Solution (in PYTHON):

Solution:
n=input()
lst=map(int,raw_input().split())
lst2=sorted(lst)
c=[]
lst3=[]
for i in range(0,max(lst)+2):
    lst3.append(['0'])
#lst3=['0']*(max(lst)+2)
#print lst3
if(1==1):
    for i in range(0,n):
        
        
        (lst3[lst[i]]).append(str(i))
        #print lst3[lst[i]]
    
    lst4=[]
    #print lst3
    for i in range(0,len(lst3)):
        if(lst3[i]!=["0"]):
            lst4.append((i,lst3[i]))
    l=len(lst4)
    #print lst4
    #print lst3
    lst5=[0]*n
    lst6=[]
    #print lst4
    for i in range(0,l):
        s2=lst4[i]
        s=s2[1]
        c=s2[0]
        lst6.append(c)
        #print s
        for j in range(1,len(s)):
            lst5[int(s[j])]=i+1
nc=0
nc2=0
m=len(lst6)
for x in range(0,m):
    if(x<len(lst6) and lst6[x]-1<len(lst5)and lst6[x]-1>=0):
        
        if(lst5[lst6[x]-1]==x+1):
            nc=nc+1
#print nc
for x in range(0,n):
    #print lst5[x]-1,len(lst6)
    if(x<len(lst5) and x<len(lst) and lst5[x]-1<len(lst6) and lst5[x]-1>=0 ):
        #print lst5[x]-1,len(lst6)
        if(lst6[lst5[x]-1]==lst[x]):
            nc2=nc2+1
if(nc==m and nc2==n):
    print len(lst6)
    for i in range(0,n):
        print lst5[i],
    print 
    for i in range(0,len(lst6)):
        print lst6[i],
else:
    print -1