Problem Statement

Consider strings of length $N$ consisting of A, B, and C. Among them, find the number of strings that satisfy the following condition, modulo $2$:

• Let $S_i$ be the string formed by the first $i$ characters of $S$. Also let $A_i$, $B_i$, and $C_i$ be the numbers of A's, B's, and C's in $S_i$, respectively. For all $i$ such that $1 \le i \le N$, the following holds:
• $A_i-B_i \le X$
  • $B_i-C_i \le Y$
  • $C_i-A_i \le Z$

You have $T$ test cases to solve.

Constraints

• $1 \le T \le 10$
• $1 \le N \le 10^9$
• $0 \le X,Y,Z \le 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

T
\mathrm{case}_1
\mathrm{case}_2
\vdots
\mathrm{case}_T

Each case is in the following format:

N X Y Z

Output

For each case, print the answer.