201475: [AtCoder]ARC147 F - Again ABC String

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.

Sample Input 1

1
3 2 1 0

Sample Output 1

0

$8$ strings satisfy the condition: AAB,AAC,ABA,ABC,ACA,ACB,BAA,BAC. Therefore the answer is $0$.

Sample Input 2

10
1 22 9 92
14 7 74 39
23 50 8 6
93 40 9 60
68 8 47 64
11 68 18 24
3 26 54 8
46 17 90 86
86 76 45 55
80 68 79 62

Sample Output 2

1
0
0
0
1
1
1
0
1
0