Total Components solution codechef

Total Components solution codechef

You are given all N1N−1 integers in the range [2,N][2,N]. In each step, you choose 22 distinct integers and if they share a common factor greater than 11, you combine them into the same group. You keep doing it until no further merging is possible.

Belonging to a group is an equivalence relation. So if integers aa and bb are in the same group and integers bb and cc are in the same group, then integers aa and cc are also said to be in the same group.

Find the total number of groups formed in the end.

Input Total Components solution codechef

  • First line will contain TT, number of test cases. Then the test cases follow.
  • Each test case contains a single line of input, a single integer NN.

Output Total Components solution codechef

For each test case, output in a single line the answer to the problem.

Constraints Total Components solution codechef

  • 1T21051≤T≤2⋅105
  • 2N1072≤N≤107

Subtasks

Subtask #1 (30 points):

  • 1T2001≤T≤200
  • 2N10002≤N≤1000

Subtask #2 (70 points): original constraints

Sample Input Total Components solution codechef

3
2
4
8

Sample Output v Total Components solution codechef

1
2
3

Explanation Total Components solution codechef

Test Case 11: The final group is {2}{2}.

Test Case 22: The final groups are {2,4}{2,4}, and {3}{3}.

Test Case 33: The final groups are {2,3,4,6,8}{2,3,4,6,8}{5}{5}, and {7}{7}.

SOLUTION

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