# Internet Problem Solving Contest

## Problem P – Partitioning a square

In this problem you are given a number n and your task is to produce a square of letters.

The square must have the following properties:

• Each letter is one of the first n lowercase English letters (`a`-`z`).
• Each of those n letters occurs the same number of times.
• All occurrences of each letter form one 4-connected region (explained below).
• The square is as small as possible.

We say that the occurrences of some letter X form a 4-connected region if it is possible to travel from any X to any other X by only moving one step up/down/left/right at a time without stepping onto a letter other than X.

Below is an example of a 6 × 6 square divided into n = 4 equally large 4-connected regions. (Note that this is not the smallest possible square that can be divided into 4 regions.)

``````aaaaab
aaaabb
bbbbbd
bddddd
cdddcc
cccccc``````

### Input specification

The first line of the input file contains an integer t specifying the number of test cases. Each test case is preceded by a blank line.

Each test case consists of a single line with a single positive integer n.

In the easy subproblem P1 we have t = 1 and the only test case has n = 4.

In the hard subproblem P2 we have t ≤ 50 and each n is between 1 and 26, inclusive.

### Output specification

For each test case, output several lines. The first of those lines should contain an integer s: the side length of your square. The rest of the output for that test case should consist of s lines, each containing s lowercase letters.

### What to submit

Do not submit any programs. Your task is to produce and submit the correct output files `p1.out` and `p2.out` for the provided input files `p1.in` and `p2.in`.

### Example

Input:

``````1

2``````

Output:

``````2
ab
ab``````