Business Matters#12238

Business Matters

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Taras, as a true businessman, has business matters to attend to. Today, he needs to visit two offices and resolve issues in each of them. However, there's a problem: he is not sure if he will be able to solve everything today.

He starts at home at time $0$ . The first office is open in the time range $[q_{1}, q_{2}]$ [q_1, q_2]. Resolving issues there will take $t_{1}$ t_1 time. The second office is open in the range $[w_{1}, w_{2}]$ [w_1, w_2]. Resolving issues there will take $t_{2}$ t_2 time. If, upon his arrival at the office, there is less time left before it closes than is needed to resolve the issues, he will not be able to solve them. Additionally, moving between locations also takes time. Traveling from home to the first office and back takes $r_{1}$ r_1 time. Traveling from home to the second office and back takes $r_{2}$ r_2 time. Traveling between the offices in either direction takes $r_{3}$ r_3 time. If he arrives at the office before it opens, he can wait until the office starts working.

Tell Taras whether he will be able to resolve his issues today.

Input

The first line contains a single integer $t$ $(1 \leq t \leq 1 0^{4})$ (1 \le t \le 10^4) — the number of test cases.

Each test case consists of three lines.

The first line contains three integers $r_{1}, r_{2}, r_{3}$ r_1, r_2, r_3 $(0 \leq r_{1}, r_{2}, r_{3} \leq 1 0^{9})$ (0 \le r_1,r_2,r_3 \le 10^9) — the time Taras spends traveling to the first office from home and back, the time spent traveling to the second office from home and back, and the time Taras spends moving between the offices in either direction, respectively. It is guaranteed that $r_{1} + r_{3} \geq r_{2}$ r_1 + r_3 \ge r_2, $r_{2} + r_{3} \geq r_{1}$ r_2 + r_3 \ge r_1, and $r_{1} + r_{2} \geq r_{3}$ r_1+r_2 \ge r_3.

The second line contains three integers $q_{1}, q_{2}, t_{1}$ q_1, q_2, t_1 $(0 \leq q_{1} \leq q_{2} \leq 1 0^{9}, 0 \leq t_{1} \leq 1 0^{9})$ (0 \le q_1 \le q_2 \le 10^9, 0 \le t_1 \le 10^9) — the time interval during which the first office is open and the amount of time Taras needs to resolve issues in the first office.

The third line contains three integers $w_{1}, w_{2}, t_{2}$ w_1, w_2, t_2 $(0 \leq w_{1} \leq w_{2} \leq 1 0^{9}, 0 \leq t_{2} \leq 1 0^{9})$ (0 \le w_1 \le w_2 \le 10^9, 0 \le t_2 \le 10^9) — the time interval during which the second office is open and the amount of time Taras needs to resolve issues in the second office.

Output

For each test case, output $1$ if Taras can resolve all matters or $0$ if he cannot.

Examples

Example 1

Note

For the first test case, Taras can first go the distance $r_{1}$ r_1 to the first office and wait until time $7$ . He will finish all matters at time $9$ and then travel the distance $r_{3}$ r_3 to the second office. He will arrive there at time $12$ and finish all matters in it at time $15$ .

Scoring

Subtask $1$ ( $10$ points): $(r_{1} = r_{2} = r_{3})$ (r_1 = r_2 = r_3)
Subtask $2$ ( $10$ points): $(t_{1} = t_{2} = 0)$ (t_1 = t_2 = 0)
Subtask $3$ ( $10$ points): $(q_{1} \leq q_{2} < w_{1} \leq w_{2})$ (q_1 \le q_2 < w_1 \le w_2)
Subtask $4$ ( $20$ points): No additional constraints