User ainta likes trees. This time he is going to make an undirected tree with *n* vertices numbered by integers from 1 to *n*. The tree is weighted, so each edge of the tree will have some integer weight.

Also he has an array *t*: *t*[1], *t*[2], ..., *t*[*n*]. At first all the elements of the array are initialized to 0. Then for each edge connecting vertices *u* and *v* (*u* &lt; *v*) of the tree with weight *c*, ainta adds value *c* to the elements *t*[*u*], *t*[*u* + 1], ..., *t*[*v* - 1], *t*[*v*] of array *t*.

Let's assume that *d*(*u*, *v*) is the total weight of edges on the shortest path between vertex *u* and vertex *v*. User ainta calls a pair of integers *x*, *y* (1 ≤ *x* &lt; *y* ≤ *n*) good if and only if *d*(*x*, *y*) = *t*[*x*] + *t*[*x* + 1] + ... + *t*[*y* - 1] + *t*[*y*].

User ainta wants to make at least <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ff3debcd979cb1dbc17aecf1e75e31f997a019f8.png" style="max-width: 100.0%;max-height: 100.0%;"/> good pairs, but he couldn't make a proper tree. Help ainta to find such a tree.
The first line contains a single integer *n* (5 ≤ *n* ≤ 10<sup class="upper-index">5</sup>).
print("_RANDOM_GUESS_1689432638.875712")# 1689432638.875731