Problem Statement

A triangle $ABC$ on the $xy$-plane is said to be a good triangle when it satisfies all of the following conditions.

• Each of the vertices $A$, $B$, and $C$ is a lattice point whose $x$- and $y$-coordinates are between $0$ and $10^{8}$, inclusive.
• The triangle $ABC$ (including the perimeter and vertices) wholly contains exactly one square of area $1$ whose vertices are all lattice points.

You are given a positive integer $S$.

Determine if there is a good triangle of area $\frac{S}{2}$, and construct one if it exists.

For each input file, you have $T$ test cases to solve.

Constraints

• $1\leq T\leq 10^{5}$
• $1\leq S\leq 10^{8}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\text{case}_{1}
\text{case}_{2}
\vdots
\text{case}_{T}

Each case is given in the following format:

S

Output

For each case, print No if there is no good triangle of area $\frac{S}{2}$, and such a triangle in the following format if there is one.

Yes
AX AY BX BY CX CY

Here, $AX$, $BX$, $CX$ are the $x$-coordinates of $A$, $B$, $C$, and $AY$, $BY$, $CY$ are the $y$-coordinates of $A$, $B$, $C$, respectively.

When printing Yes or No, you may use either uppercase or lowercase English letters. If multiple solutions exist, any of them will be accepted.