[Solution] OR Tuples CodeChef Solution

Problem

Chef has $3$ numbers $P$, $Q$ and $R$. Chef wants to find the number of triples $(A, B, C)$ such that:

• $(A \mid B) = P,$ $(B \mid C) = Q$ and $(C \mid A) = R$ (Here, $\mid$ denotes the bitwise OR operation)
• $0 \le A, B, C \lt 2^{20}$

Can you help Chef?

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of a single line of input containing $3$ space-separated integers denoting $P, Q$ and $R$

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•  respectively.

Output Format

For each test case, output a single integer denoting the number of triplets $(A, B, C)$ that satisfy the given conditions.

Explanation:

Test case $1$: The following $4$ triplets $(A, B, C)$ satisfy $A \mid B = 10, B\mid C = 12,$ and $C\mid A = 14$: $(2, 8, 12), (10, 0, 12), (10, 8, 4),$ and $(10, 8, 12)$.

Test case $2$: The following triplet $(A, B, C)$ satisfies $A \mid B = 0, B\mid C = 5,$ and $C\mid A = 5$: $(0, 0, 5)$.

Test case $3$: There are no triplets satisfying all the conditions.