Binary associativity

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Basic Programming, Basics of Implementation, Easy, Implementation

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Problem

A binary operation $*$ on a set $S$ is called associative if it satisfies the associative law: $(x * y) * z = x * (y * z)$ for all $x$ , $y$ , $z$ in $S$ .

For the binary set $S = \{0, 1\}$ and a particular binary operator $*$ , you are given its truth table. Determine if the operation is associative.

$a$	$b$	$a * b$
$0$	$0$	$c_{0}$
$0$	$1$	$c_{1}$
$1$	$0$	$c_{2}$
$1$	$1$	$c_{3}$

Input format

First line: A single integer $T$ denoting the number of test cases
For each test case:
- First line: Four space-separated integers $c_{0}, c_{1}, c_{2}, c_{3}$

Output format

For each test case, print 'Yes' (without quotes) in a new line if the binary operation is associative in nature. Otherwise, print 'No' (without quotes).

Constraints

$1 \le T \le 8$

$c_0, c_1, c_2, c_3 \in \{ 0, 1 \}$

Time Limit: 1

Memory Limit: 256

Source Limit:

Explanation

The given operation is the binary xor. It can be easily proved that it is associative.