CF398C.Tree and Array

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 < 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 < 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 good pairs, but he couldn't make a proper tree. Help ainta to find such a tree.

用户 ainta 喜欢树。这次他要构造一棵包含 $ n $ 个顶点的无向树，顶点编号为 $ 1 $ 到 $ n $。该树是带权的，因此树中的每条边都具有某个整数权重。

此外，他还拥有一个数组 $ t $：$ t[1],,t[2],,\dots,,t[n] $。初始时，数组中所有元素均设为 $ 0 $。接着，对于树中任意一条连接顶点 $ u $ 和 $ v $（其中 $ u < v $）且权重为 $ c $ 的边，ainta 将值 $ c $ 加到数组 $ t $ 的元素 $ t[u],,t[u+1],,\dots,,t[v-1],,t[v] $ 上。

设 $ d(u,,v) $ 表示顶点 $ u $ 与顶点 $ v $ 之间最短路径上所有边的权重之和。用户 ainta 称一对整数 $ x,,y $（满足 $ 1 \le x < y \le n $）为“好”的，当且仅当

$$d(x,\,y) = t[x] + t[x+1] + \dots + t[y-1] + t[y].$$

用户 ainta 希望构造出至少 对“好”的数对，但他未能成功构造出满足条件的树。请帮助 ainta 找到这样一棵树。

The first line contains a single integer n (5 ≤ n ≤ 105).

第一行包含一个整数 $n$（$5 \le n \le 10^5$）。

Print n - 1 lines containing the description of the edges. The i-th line should contain three space-separated integers u__i, v__i, c__i (1 ≤ u__i < v__i ≤ n; 1 ≤ c__i ≤ 105) — two vertices connected by the edge, and the weight of the edge.

Next print lines containing the good pairs. The k-th line should contain two space-separated integers x__k and y__k (1 ≤ x__k < y__k ≤ n). Of course, x__k, y__k must be a good pair. All pairs should be distinct — that is, for all j, k , x__j ≠ x__k or y__j ≠ y__k must be satisfied.

If there are many correct solutions, print any of them.

输出 n - 1 行，每行描述一条边。第 i 行应包含三个以空格分隔的整数 u__i, v__i, c__i（其中 1 ≤ u__i < v__i ≤ n；1 ≤ c__i ≤ 10⁵），分别表示该边所连接的两个顶点及其权重。

接下来输出 行，每行描述一个“好对”（good pair）。第 k 行应包含两个以空格分隔的整数 x__k 和 y__k（其中 1 ≤ x__k < y__k ≤ n）。显然，(x__k, y__k) 必须是一个好对。所有输出的好对必须互不相同——即对任意 j, k，需满足 ，x__j ≠ x__k 或 y__j ≠ y__k。

若存在多个正确解，输出任意一个即可。

⌊x⌋ is the largest integer not greater than x.

You can find the definition of a tree by the following link: http://en.wikipedia.org/wiki/Tree_(graph_theory)

You can also find the definition of the shortest path by the following link: http://en.wikipedia.org/wiki/Shortest_path_problem

The tree and the array t in the sample output look like this:

⌊x⌋ 是不大于 x 的最大整数。

树的定义可参考以下链接：http://en.wikipedia.org/wiki/Tree_(graph_theory)

最短路径的定义可参考以下链接：http://en.wikipedia.org/wiki/Shortest_path_problem

样例输出中的树和数组 t 如下图所示：