103442: [Atcoder]ABC344 C - A+B+C

Problem Statement

You are given three sequences $A=(A_1,\ldots,A_N)$, $B=(B_1,\ldots,B_M)$, and $C=(C_1,\ldots,C_L)$.

Additionally, a sequence $X=(X_1,\ldots,X_Q)$ is given. For each $i=1,\ldots,Q$, solve the following problem:

Problem: Is it possible to select one element from each of $A$, $B$, and $C$ so that their sum is $X_i$?

Constraints

• $1 \leq N,M,L \leq 100$
• $0 \leq A_i, B_i ,C_i \leq 10^8$
• $1 \leq Q \leq 2\times 10^5$
• $0 \leq X_i \leq 3\times 10^8$
• All input values are integers.

Input

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

$N$
$A_1$ $\ldots$ $A_N$
$M$
$B_1$ $\ldots$ $B_M$
$L$ 
$C_1$ $\ldots$ $C_L$
$Q$
$X_1$ $\ldots$ $X_Q$

Output

Print $Q$ lines. The $i$-th line should contain Yes if it is possible to select one element from each of $A$, $B$, and $C$ so that their sum is $X_i$, and No otherwise.

Sample Input 1

3
1 2 3
2
2 4
6
1 2 4 8 16 32
4
1 5 10 50

Sample Output 1

No
Yes
Yes
No

• It is impossible to select one element from each of $A$, $B$, and $C$ so that their sum is $1$.
• Selecting $1$, $2$, and $2$ from $A$, $B$, and $C$, respectively, makes the sum $5$.
• Selecting $2$, $4$, and $4$ from $A$, $B$, and $C$, respectively, makes the sum $10$.
• It is impossible to select one element from each of $A$, $B$, and $C$ so that their sum is $50$.