Total Components Solution Codechef -You are given all N−1N−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

 

Total Components Solution Codechef -  

SOLUTION

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You are given all N−1$N-1$ integers in the range [2,N]$[2,N]$. In each step, you choose 2$2$ distinct integers and if they share a common factor greater than 1$1$, 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 a$a$ and b$b$ are in the same group and integers b$b$ and c$c$ are in the same group, then integers a$a$ and c$c$ are also said to be in the same group.

Find the total number of groups formed in the end.

Input

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

Output

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

Constraints

• 1≤T≤2⋅105$1\le T\le 2\cdot {10}^5$
• 2≤N≤107$2\le N\le {10}^7$

Subtasks

Subtask #1 (30 points):

• 1≤T≤200$1\le T\le 200$
• 2≤N≤1000$2\le N\le 1000$

Subtask #2 (70 points): original constraints

Sample Input

3
2
4
8

Sample Output

1
2
3

Explanation

Test Case 1$1$: The final group is {2}$\{2\}$.

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

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

Date Added:28-05-2021

Time Limit:1 secs

Source Limit:50000 Bytes

Languages:CPP14, C, JAVA, PYTH 3.6, PYTH, CS2, ADA, PYPY, PYP3, TEXT, CPP17, PAS fpc, RUBY, PHP, NODEJS, GO, TCL, HASK, PERL, SCALA, kotlin, BASH, JS, PAS gpc, BF, LISP sbcl, CLOJ, LUA, D, R, CAML, rust, ASM, FORT, FS, LISP clisp, SQL, swift, SCM guile, PERL6, CLPS, WSPC, ERL, ICK, NICE, PRLG, ICON, PIKE, COB, SCM chicken, SCM qobi, ST, NEM, SQLQ

SOLUTION

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