Cuber QQ has challenged you with the task to construct a binary tree with root 1, and no more than 5000 nodes, along with a divide-and-conquer strategy, such that the recursive depth d of your divide-and-conquer strategy is at least 2 levels less than the strategy based on sizes of subtrees.

The recursive depth d of a function is defined as the maximum number of functions ever appeared in the call stack (see the return value of the pseudo-code below for a formal definition).

The divide-and-conquer strategy based on subtree sizes is shown as below:



Note: In this pseudo-code, denotes a subtree in T whose root is u.

No input.

In the first line, output an positive integer n (), which is the node number of your binary tree.

In the following n-1 lines, output  and  in the i-th line, denoting an edge connecting  and .

Cuber QQ will delete the edge one by one in the order that you give in the output, starting from , and recursively handle the subtrees.