Problem Statement

First, let us introduce some terminology. A $(1,5)$-digit decimal representation of a real number $x$ is a decimal representation of $x$ whose integer part and fractional part have $1$ digit and $5$ digits, respectively.

An approximate $3$rd root of a real square matrix $M$ of order $2$ is a real square matrix $N$ of order $2$ satisfying both of the following $2$ conditions:

1. The absolute value of each entry of $M - N^3$ is less than $10^{-3}$.
2. Each entry of $N$ has a $(1,5)$-digit decimal representation.

Now, consider the following problem:

A real symmetric matrix $M$ of order $2$ is given as input.

Determine whether an approximate $3$rd root of $M$ exists, and if it exists, find $1$ of them.

A positive integer $T$ is given at the beginning of the input. Answer $T$ problems.

Input

Below, for each positive integer $t$ at most $T$, the input for the $t$-th problem is denoted by $M_t$. Also, for a real square matrix $M$ of order $2$ and positive integers $i,j$ at most $2$, $M_{i,j}$ denotes the $(i,j)$ entry of $M$.

The input is given from standard input in $1 + 2T$ lines in the following format:

• Line $1$ contains $T$.
• For each positive integer $t$ at most $T$, lines $2t$ through $2t+1$ contain the input for the $t$-th problem.

$T$
($1$ 個目の問題に対する入力)
$\vdots$
($T$ 個目の問題に対する入力)

Here, for each positive integer $t$ at most $T$, the input for the $t$-th problem is given from standard input in $2$ lines (lines $2t$ through $2t + 1$ of the entire input) in the following format:

• Line $1$ contains $(1,5)$-digit decimal representations of $(M_t)_{1,1}, (M_t)_{1,2}$, separated by a single-byte space.
• Line $2$ contains $(1,5)$-digit decimal representations of $(M_t)_{2,1}, (M_t)_{2,2}$, separated by a single-byte space.

$(M_t)_{1,1}$ $(M_t)_{1,2}$
$(M_t)_{2,1}$ $(M_t)_{2,2}$

Constraints

The input satisfies the following constraints:

• $T$ is a positive integer satisfying $1 \leq T \leq 10^5$.
• For each positive integer $t$ at most $T$, the input $M_t$ for the $t$-th problem satisfies the following:
• $M_t$ is a real symmetric matrix of order $2$.
• Each entry of $M_t$ has a $(1,5)$-digit decimal representation.

Output

For each positive integer $t$ at most $T$, print the answer to the $t$-th problem on lines $2t-1$ and $2t$ in the following format:

• If no approximate $3$rd root of $M_t$ exists, print No on both line $2t-1$ and line $2t$.

No
No

• If an approximate $3$rd root of $M_t$ exists, let $N_t$ be $1$ of them, and:
• On line $2t-1$, print $(1,5)$-digit decimal representations of $(N_t)_{1,1}, (N_t)_{1,2}$, separated by a single-byte space.
• On line $2t$, print $(1,5)$-digit decimal representations of $(N_t)_{2,1}, (N_t)_{2,2}$, separated by a single-byte space.

$(N_t)_{1,1}$ $(N_t)_{1,2}$
$(N_t)_{2,1}$ $(N_t)_{2,2}$

This problem uses a special judge. There may be more than $1$ correct answer, but print only $1$ of them.

Print a newline at the end.

Sample

1
0.00000 0.00000
0.00000 0.00000

0.00000 0.00000
0.00000 0.00000

0.00001 0.00001
0.00001 0.00001

0.00000 9.99999
-0.00000 0.00000

1
1.00000 0.00000
0.00000 1.00000

1.00000 0.00000
0.00000 1.00000

2
1.00000 0.00000
0.00000 -1.00000
1.00000 -0.00000
-0.00000 -1.00000

1.00000 0.00000
0.00000 -1.00000
1.00000 -0.00000
-0.00000 -1.00000