Sengoku still remembers the mysterious "colourful meteoroids" she discovered with Lala-chan when they were little. In particular, one of the nights impressed her deeply, giving her the illusion that all her fancies would be realized.

On that night, Sengoku constructed a permutation p_1, p_2, ..., p_{n} of integers from 1 to n inclusive, with each integer representing a colour, wishing for the colours to see in the coming meteor outburst. Two incredible outbursts then arrived, each with n meteorids, colours of which being integer sequences a_1, a_2, ..., a_{n} and b_1, b_2, ..., b_{n} respectively. Meteoroids' colours were also between 1 and n inclusive, and the two sequences were not identical, that is, at least one i (1 ≤ i ≤ n) exists, such that a_{i} ≠ b_{i} holds.

Well, she almost had it all — each of the sequences a and b matched exactly n - 1 elements in Sengoku's permutation. In other words, there is exactly one i (1 ≤ i ≤ n) such that a_{i} ≠ p_{i}, and exactly one j (1 ≤ j ≤ n) such that b_{j} ≠ p_{j}.

For now, Sengoku is able to recover the actual colour sequences a and b through astronomical records, but her wishes have been long forgotten. You are to reconstruct any possible permutation Sengoku could have had on that night.

-----Input-----

The first line of input contains a positive integer n (2 ≤ n ≤ 1 000) — the length of Sengoku's permutation, being the length of both meteor outbursts at the same time.

The second line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ n) — the sequence of colours in the first meteor outburst.

The third line contains n space-separated integers b_1, b_2, ..., b_{n} (1 ≤ b_{i} ≤ n) — the sequence of colours in the second meteor outburst. At least one i (1 ≤ i ≤ n) exists, such that a_{i} ≠ b_{i} holds.

-----Output-----

Output n space-separated integers p_1, p_2, ..., p_{n}, denoting a possible permutation Sengoku could have had. If there are more than one possible answer, output any one of them.

Input guarantees that such permutation exists.

-----Examples-----

Input 5 1 2 3 4 3 1 2 5 4 5

Output 1 2 5 4 3

Input 5 4 4 2 3 1 5 4 5 3 1

Output 5 4 2 3 1

Input 4 1 1 3 4 1 4 3 4

Output 1 2 3 4

-----Note-----

In the first sample, both 1, 2, 5, 4, 3 and 1, 2, 3, 4, 5 are acceptable outputs.

In the second sample, 5, 4, 2, 3, 1 is the only permutation to satisfy the constraints.