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()
f = [0]
f.extend(map(int, raw_input().split()))


for v in f:
	if f[v] != v:
		print -1
		break
else:
	size = len(f)
	m = 0
	g = [0] * size
	h = [0] * size
	f_to_m_map = [0] * size
	for i in xrange(1, size):
		v = f[i]
		if f_to_m_map[v] == 0:
			m += 1
			f_to_m_map[v] = m
			h[m] = v
		g[i] = f_to_m_map[v]
	print m
	print ' '.join(map(str, g[1:]))
	print ' '.join(map(str, h[1:m+1]))