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 PYTHON3):

Solution:
import sys

n = int(input())
s = input().split()
a = [int(i) for i in s]
a.insert(0,0)

hash = [0 for i in range(n+1)]
g = [0 for i in range(n+1)]
h = [0 for i in range(n+1)]
index = 1

for i in range(1, n+1):
	if hash[a[i]] == 0:
		if index>n:
			print(-1)
			exit()
		hash[a[i]]=index
		g[i] = index
		h[index] = a[i]
		index+=1
	else:
		g[i] = hash[a[i]]
		
for i in range(1,index):
	if g[h[i]]!=i:
		print(-1)
		exit()

print(index-1)
print(' '.join([str(i) for i in g[1:n+1]]))
print(' '.join([str(i) for i in h[1:index]]))