Artificial Elements

Interview

Time limit1sMemory limit256 MB

Summary

For each atomic number up to 118, decide whether it can be written as the sum of two prime numbers.

Level: Easy3 of 10
Topics: Number theory, Brute force
Solved: No attempts yet

Problem

Element 43, technetium, is the first artificially produced radioactive element and the lightest radioactive element. Technetium was first discovered through artificial synthesis rather than in nature. It was reportedly produced by bombarding molybdenum, which has atomic number 42, with particles.

Wondering which property of technetium made this artificial synthesis possible, Junik thought long and hard and came up with an absurd hypothesis: the reason lies in atomic numbers that can be written as the sum of two prime numbers. Impressed by his own discovery, Junik wants to check whether each element can be synthesized artificially. Help Junik by determining, for each given atomic number, whether the element can be synthesized artificially.

Input

The first line contains the number of atomic numbers to ask about, $N$ . ( $1 \le N \le 118$ )

Each of the next $N$ lines contains an atomic number $a$ . ( $1 \le a \le 118$ )

No atomic number is given more than once.

Output

For each atomic number, print Yes if the element with that atomic number can be synthesized artificially, or No otherwise. Print one answer per line in the given order.

Examples1

Example 1
Input
```
3
2
5
19
```
Expected output
```
No
Yes
Yes
```