Gone bananas | Practice Problems

Gone bananas

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2.2

17 votes

Easy, Grammar-Verified, Math, Number Theory, Primality test, Prime number

Details

Problem

You are required to distribute $N$ bananas among some people according to the following conditions:

You can select the number of people that receive bananas.
Each person should get more than one banana.
One person cannot receive all the bananas.
All the $N$ bananas must be distributed.
Each person can only receive an integral number of bananas.

Write a program to determine whether the bananas can be distributed among the people.

Input format

First line: $T$ denoting the number of test cases
Next $T$ lines: $N$

Output format

For each test case, print $Yes$ or $No$ depending upon the result.

Constraints

$2 \le T \le 10^5$
$1 \le N \le 10^6$

Sample Input

2
2
4

Sample Output

No
Yes

Time Limit: 1

Memory Limit: 256

Source Limit:

Explanation

Explanation of the first test case:
$2$ bananas cannot be distributed among a group of any size. Suppose a group of size $1$ is considered, then one person takes all the bananas. If a group of size $2$ , then each person get only $1$ banana that violates the rule of distribution.
Explanation of the second test case:
$4$ bananas can be equally distributed among $2$ people where each person gets $2$ bananas.

Contributers:

Mohit Anand

Rivu Das