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Settlers of Catan

1000ms 65536K

Description:

The popular board game \Settlers of Catan" starts by creating a random board. This board consists of hexagonal resource tiles containing ve di erent resources: clay, lumber, wool, grain, and ore. For simplicity, we will denote these by the numbers 1 to 5.

Random boards, however, often have multiple equal resource tiles next to each other. This annoys some players. Therefore, we have invented a new way of creating the playing board. Starting in the middle and spiraling outwards, each time we add a new tile to the board we choose the resource of the tile according to the following rules:

 the new tile must be di erent from its neighboring tiles on the board so far;

 in case multiple tiles are possible, we choose a resource that occurs the least number of times on the board so far;

 in case multiple tiles are still possible, the new resource must have the lowest number possible.


The fi gure underneath shows how to spiral outwards and which resource tiles are chosen rst. We are curious what the number of the resource is on the nth tile that is added to the board (starting with n = 1).

Input:

On the rst line of the input there is one integer c (1 <= c <= 200), the number of test cases. Each following test case consists of a single line with one integer n (1 <= n <= 10 000), the number of the tile we are curious about.


Output:

For each test case, print a single line with one integer, specifying the resource of the nth tile.

Sample Input:

4
1
4
10
100

Sample Output:

1
4
5
5

Note:

本题由旧版NOJ导入,来源:NWERC2009

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NOJ

Provider NOJ

Code NOJ1195

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Date 04/20/2019 10:03:10

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