Sum equals LCM

AtCoder

IDarc165_a

Time2000ms

Memory256MB

Difficulty—

You are given a positive integer $N$. Determine if there are two or more (not necessarily distinct) positive integers $A_1,A_2,\dots,A_n\ (2 \leq n)$ that satisfy all of the following conditions: * $A_1+A_2+\dots+A_n=N$. * The least common multiple of $A_1,A_2,\dots,A_n$ is $N$. You have $T$ test cases to solve. ## Constraints * $1 \leq T \leq 100$ * $2 \leq N \leq 10^{9}$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\vdots$ $\mathrm{case}_T$ Each case is given in the following format: $N$ [samples]

Samples

Input #1

Output #1

Yes
No
No
Yes

For the first test case, three positive integers $(A_1,A_2,A_3)=(1,2,3)$, for example, have $A_1+A_2+A_3=1+2+3=6$, and the least common multiple of $A_1,A_2,A_3$ is $6$, satisfying the conditions.
For the second test case, no two or more positive integers satisfy the conditions.

API Response (JSON)

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