UVa 10161 Ant on a Chessboard：简单数学

UVa 10161 Ant on a Chessboard：简单数学2014-07-16 synapse7 10161 - Ant on a Chessboard

Time limit: 3.000 seconds

http://uva.onlinejudge.org/index.php？option=com_onlinejudge&Itemid=8&category=99&page=show_problem&problem=1102

Background

One day, an ant called Alice came to an M*M chessboard. She wanted to go around all the grids. So she began to walk along the chessboard according to this way: （you can assume that her speed is one grid per second）

At the first second, Alice was standing at （1,1）. Firstly she went up for a grid, then a grid to the right, a grid downward. After that, she went a grid to the right, then two grids upward, and then two grids to the left…in a word, the path was like a snake.

For example, her first 25 seconds went like this:

（ the numbers in the grids stands for the time when she went into the grids）

At the 8th second , she was at （2,3）, and at 20th second, she was at （5,4）.

Your task is to decide where she was at a given time.

（you can assume that M is large enough）

Input

Input file will contain several lines, and each line contains a number N（1<=N<=2*10^9）, which stands for the time. The file will be ended with a line that contains a number 0.

Output

For each input situation you should print a line with two numbers （x, y）, the column and the row number, there must be only a space between them.

Sample Input

Sample Output

2 3

5 4

1 5

题意：找到数字对应的行和列。

思路：找规律，奇数行，起始为行数的平方。偶数列，起始为列数的平方。行和列有与数字匹配的规律。依次确定所在的行和列。