There is a variable (sum), which is initially equal to (0). There is also a data structure that can perform the following operations: pushback x — adds an element with value (x) to the end of the structure; pushfront x — adds an element with value (x) to the beginning of the structure; popback — removes the last element from the structure; popfront — removes the first element from the structure; min — adds the value of the minimum element currently in the structure to the variable (sum). The operations popback , popfront , and min cannot be applied to an empty structure! Using this structure, you would like to be able to find the sum of the minimums of all non-empty subarrays of an array (a) of (n) elements. More formally, your task is to find a sequence of no more than (n \cdot (n + 2)) commands such that after all operations, the variable (sum) will be equal to (\sum_{0 \le l \le r < n} \min(al,\dots, ar)) for any possible array (a). The first line contains a single integer (n) ((1 \le n \le 500)) — the number of elements in the array. Output (k) ((1 \le k \le n \cdot (n + 2))) commands. Each command must be one of the following five lines: " pushback ai ", where (i) — a number from (0) to (n - 1) " pushfront ai ", where (i) — a number from (0) to (n - 1) " popback " " popfront " " min " If there are multiple valid answers, output any.