Four Pieces, One Sheet - Repovive Standard Round 7 | Repovive

22A. Four Pieces, One Sheet

500 pts1s256 MB

A rectangular sheet has been divided into four rectangles by one horizontal cut and one vertical cut. Each cut goes all the way from one edge of the sheet to the opposite edge, and the pieces are not moved between the cuts.

You are given four positive integers $a$ , $b$ , $c$ , and $d$ . Determine whether the areas of the four pieces can be these numbers, in any order.

The dimensions of the sheet and the positions of the cuts can be chosen freely; they do not have to be integers.

Constraints

$1 \le t \le 10^4$
$1 \le a,b,c,d \le 10^9$

Input

The first line contains the number of test cases $t$ . Each test case consists of one line containing $a$ , $b$ , $c$ , and $d$ .

t

\left. \begin{array}{l} a \quad b \quad c \quad d \end{array} \right\} \times t

Output

For each test case, output $\texttt{"Yes"}$ if such a sheet and cuts exist, or $\texttt{"No"}$ otherwise.

You may print each letter in any case. For example, $\texttt{"Yes"}$ , $\texttt{"YES"}$ , and $\texttt{"YeS"}$ are all accepted.

\left. \begin{array}{l} \texttt{Yes / No} \end{array} \right\} \times t

Samples

Input

Case 1

1 1 1 1

Case 2

1 2 3 4

Case 3

6 15 10 25

Case 4

1 1 1 2

Case 5

2 3 4 6

Explanation

Case 1

Take a square with side length $2$ and cut it halfway in both directions. All four pieces have area $1$ .

Case 2

No choice of a rectangular sheet and two cuts produces pieces with areas $1$ , $2$ , $3$ , and $4$ .

Case 3

Take a sheet of width $8$ and height $7$ . Split its width into $3$ and $5$ , and its height into $2$ and $5$ . The piece areas are $6$ , $10$ , $15$ , and $25$ .

Case 4

If three pieces all have area $1$ , the two parts of the width must be equal and the two parts of the height must also be equal. The fourth piece would then have area $1$ , not $2$ .

Case 5

Take a sheet of width $2.5$ and height $6$ . Split its width into $1$ and $1.5$ , and its height into $2$ and $4$ . The piece areas are $2$ , $3$ , $4$ , and $6$ .

Output

Case 1

Yes

Case 2

No

Case 3

Yes

Case 4

No

Case 5

Yes

You are given four positive integers $a$ , $b$ , $c$ , and $d$ . Determine whether the areas of the four pieces can be these numbers, in any order.

The dimensions of the sheet and the positions of the cuts can be chosen freely; they do not have to be integers.

$1 \le t \le 10^4$
$1 \le a,b,c,d \le 10^9$

The first line contains the number of test cases $t$ . Each test case consists of one line containing $a$ , $b$ , $c$ , and $d$ .

t

\left. \begin{array}{l} a \quad b \quad c \quad d \end{array} \right\} \times t

For each test case, output $\texttt{"Yes"}$ if such a sheet and cuts exist, or $\texttt{"No"}$ otherwise.

You may print each letter in any case. For example, $\texttt{"Yes"}$ , $\texttt{"YES"}$ , and $\texttt{"YeS"}$ are all accepted.

\left. \begin{array}{l} \texttt{Yes / No} \end{array} \right\} \times t

Take a square with side length $2$ and cut it halfway in both directions. All four pieces have area $1$ .

No choice of a rectangular sheet and two cuts produces pieces with areas $1$ , $2$ , $3$ , and $4$ .

Take a sheet of width $8$ and height $7$ . Split its width into $3$ and $5$ , and its height into $2$ and $5$ . The piece areas are $6$ , $10$ , $15$ , and $25$ .

If three pieces all have area $1$ , the two parts of the width must be equal and the two parts of the height must also be equal. The fourth piece would then have area $1$ , not $2$ .

Take a sheet of width $2.5$ and height $6$ . Split its width into $1$ and $1.5$ , and its height into $2$ and $4$ . The piece areas are $2$ , $3$ , $4$ , and $6$ .

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22A. Four Pieces, One Sheet

Constraints

Input

Output

Samples

22A. Four Pieces, One Sheet

Constraints

Input

Output

Samples