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:
from sys import stdin, stdout

n = int(stdin.readline())
f = map(int,stdin.readline().rstrip().split())

fDict={x:[] for x in f}
fSet=set(f)

for i in range(1,n+1):
    fDict[f[i-1]].append(i)

testFail=False
for i in range(1,n+1):
    if i in fSet and f[i-1]!=i:
        print -1
        testFail=True
        break

g=[0]*n
h=[0]*len(fDict.keys())
if not testFail:
    i=0
    for x in fDict.keys():
        xmap = fDict[x]
        for y in xmap:
            g[y-1]=i+1
        h[i]=x
        i+=1
    gStr = [str(x) for x in g]
    hStr = [str(x) for x in h]
    print len(h)
    print ' '.join(gStr)
    print ' '.join(hStr)