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 = int(raw_input())
out = {}
outputs = map(int, raw_input().split())
rev = {}
counter = 1
ordered_out = []
for i in xrange(n):
    if outputs[i] not in out:
        out[outputs[i]] = counter 
        rev[i] = counter
        ordered_out.append(outputs[i])
        counter+=1
    else:
        rev[i] = out[outputs[i]]
num_elts = len(out.keys())
possible = True
for i in xrange(num_elts):
    ind = ordered_out[i] - 1
    if ind not in rev or (rev[ind] != i + 1):
        possible = False
if possible:
    print num_elts
    for i in xrange(n):
        print out[outputs[i]],
    print ""
    print " ".join(map(str, ordered_out))
else: 
    print -1