# Independent Set

Time Limit: 1 Second

Memory Limit: 65536 KB

## Description

Chiaki has a positive integer m and she would like to construct a tree with at most 15 vertices in such a manner that the number of distinct nonempty independent sets is exactly m.

Note that an independent set is a subset of vertices of a graph such that every two distinct vertices are not adjacent.

## Input

There are multiple test cases. The first line of input contains an integer T (1 ≤ T ≤ 2000), indicating the number of test cases. For each test case:

The first line contains an integer m (1 ≤ m ≤ 2000).

## Output

For each test case, if there is no such graph, output -1 on a single line. Otherwise, output an integer n (1 ≤ n ≤ 15) denoting the number of vertices. Then in each of the next n - 1 lines, output two integers x and y (1 ≤ x, yn, xy) denoting an edge in the tree.

## Sample Input

5
1
2
3
10
20


## Sample Output

1
2
2 1
-1
-1
6
2 1
3 1
4 3
5 4
6 5


None

None