We are given a board of n × n squares, where n is an odd integer meeting the inequality 3 <= n < 50, and a set of k = (n² - 3) / 2 stones. Each stone has the shape of a rectangle covering exactly 2 squares of the board. The board squares are numbered consecutively by rows - the squares in the first row (from left to right) are numbered from 1 to n, the squares in the second row from n + 1 to 2n, and so on until we reach the bottom right corner square whose number is n².

We cut any three squares out of the board, and next we want to cover it with the stones. We require that every square not removed should be covered with exactly one stone (covering also one adjacent square) and that cut out squares remain uncovered.

Is it always possible?

Task

• reads from the text file SZA.IN the dimension of the board n and numbers of three board squares that have been cut out,
• examines whether such a board can be covered with stones.
  If not, the program writes the answer NIE ("no") in the file SZA.OUT.
  If so, it writes in the file SZA.OUT a sequence of k = (n² - 3) / 2 pairs of integers indicating the positions of stones covering the given board.

If there are many ways to cover the board with stones, your program should write only one (arbitrary) of them.

Input

The data in the file SZA.IN are written correctly, and your program need not verify that.

Output

• either one word NIE
• or in each of k consecutive lines two numbers separated by a space, i.e. the numbers of two adjacent squares covered with one stone.

Examples

7 17 25 40

18 19
20 21
8 9
10 11
12 13
14 7
6 5
4 3
1 2
15 22
16 23
29 36
30 37
24 31
32 39
43 44
38 45
46 47
48 49
41 42
33 34
35 28
26 27

For the file SZA.IN:

7 25 32 40

NIE

Your program should look for the file SZA.IN in the current directory and create the file SZA.OUT also in the current directory. The source file containing the program written by you should be named SZA.???, where ??? are substituted by at most three-letter abbreviation of the programming language used. The same program in an executable form should be written in a file SZA.EXE.