Refrain

Consider a sequence of n integers ranging from 1 to m. A subsequence of consecutive numbers is termed a refrain if the product of its length and the number of times it appears in the sequence is maximized.

Your task is to identify the refrain in the given sequence.

Input

The first line contains two integers n and m (1 ≤ n ≤ 150000, 1 ≤ m ≤ 10). The second line provides n integers, each between 1 and m.

Output

The first line should display the product of the refrain's length and its frequency. The second line should show the length of the refrain. The third line should present the sequence that constitutes the refrain.

Examples