There are (n) Fibonacci cubes, where the side of the (i)-th cube is equal to (f_{i}), where (f_{i}) is the (i)-th Fibonacci number. In this problem, the Fibonacci numbers are defined as follows: (f_{1} = 1) (f_{2} = 2) (f_{i} = f_{i - 1} + f_{i - 2}) for (i > 2) There are also (m) empty boxes, where the (i)-th box has a width of (w_{i}), a length of (l_{i}), and a height of (h_{i}). For each of the (m) boxes, you need to determine whether all the cubes can fit inside that box. The cubes must be placed in the box following these rules: The cubes can only be stacked in the box such that the sides of the cubes are parallel to the sides of the box; Every cube must be placed either on the bottom of the box or on top of other cubes in such a way that all space below the cube is occupied; A larger cube cannot be placed on top of a smaller cube. Each test consists of several test cases. The first line contains a single integer (t) ((1 \le t \le 10^{3})) — the number of test cases. The description of the test cases follows. In the first line of each test case, there are two integers (n) and (m) ((2 \le n \le 10, 1 \le m \le 2 \cdot 10^{5})) — the number of cubes and the number of empty boxes. The next (m) lines of each test case contain (3) integers (w_{i}), (l_{i}), and (h_{i}) ((1 \le w_{i}, l_{i}, h_{i} \le 150)) — the dimensions of the (i)-th box. Additional constraints on the input: The sum of (m) across all test cases does not exceed (2 \cdot 10^{5}). For each test case, output a string of length (m), where the (i)-th character is equal to " 1 " if all (n) cubes can fit into the (i)-th box; otherwise, the (i)-th character is equal to " 0 ". In the first test case, only one box is suitable. The cubes can be placed in it as follows: