G. Maximum Adjacent Pairs
time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given an array $$$a$$$ consisting of $$$n$$$ non-negative integers.

You have to replace each $$$0$$$ in $$$a$$$ with an integer from $$$1$$$ to $$$n$$$ (different elements equal to $$$0$$$ can be replaced by different integers).

The value of the array you obtain is the number of integers $$$k$$$ from $$$1$$$ to $$$n$$$ such that the following condition holds: there exist a pair of adjacent elements equal to $$$k$$$ (i. e. there exists some $$$i \in [1, n - 1]$$$ such that $$$a_i = a_{i + 1} = k$$$). If there are multiple such pairs for some integer $$$k$$$, this integer is counted in the value only once.

Your task is to obtain the array with the maximum possible value.

Input

The first line contains one integer $$$n$$$ ($$$2 \le n \le 3 \cdot 10^5$$$) — the number of elements in the array.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le \min(n, 600)$$$) — the elements of the array.

Output

Print $$$n$$$ integers not less than $$$1$$$ and not greater than $$$n$$$ — the array with the maximum possible value you can obtain.

If there are multiple answers, print any of them.

Examples
Input
4
1 1 0 2
Output
1 1 2 2
Input
5
0 0 0 0 0
Output
3 1 1 3 3
Input
5
1 2 3 4 5
Output
1 2 3 4 5
Input
6
1 0 0 0 0 1
Output
1 2 3 3 1 1
Input
3
3 0 2
Output
3 2 2
Input
5
1 0 2 0 1
Output
1 2 2 1 1
Input
7
1 0 2 3 1 0 2
Output
1 2 2 3 1 1 2