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:
def main():
	n = int(input())
	ar = []
	fi_values = map(int, input().strip().split())
	groups = dict()
	for i, fi in enumerate(fi_values):
		if fi not in groups:
			groups[fi] = []
		groups[fi].append(i+1)

	g = [0] * n
	h = []
	for k, v in groups.items():
		if k not in v:
			print(-1)
			return

		else:
			h.append(k)
			for i in v:
				g[i-1] = len(h)

	print(len(h))
	print(" ".join(map(str, g)))
	print(" ".join(map(str, h)))

main()