write a go solution for F. Variables and Operationstime limit per test5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputThere are n variables; let's denote the value of the i-th variable as a_i.There are also m operations which will be applied to these variables; the i-th operation is described by three integers x_i,y_i,z_i. When the i-th operation is applied, the variable x_i gets assigned the following value: min(a_x_i,a_y_i+z_i).Every operation will be applied exactly once, but their order is not fixed; they can be applied in any order.Let's call a sequence of initial variable values a_1,a_2,...,a_n stable, if no matter in which order we apply operations, the resulting values will be the same. If the resulting value of the i-th variable depends on the order of operations, then the sequence of initial variable values is called i-unstable.You have to process q queries. In each query, you will be given initial values a_1,a_2,...,a_n and an integer k; before applying the operations, you can at most k times choose a variable and decrease it by 1. For every variable i, you have to independently determine if it is possible to transform the given values into an i-unstable sequence.InputThe first line contains two integers n and m (2<=n<=500; 1<=m<=4*10^5) — the number of variables and operations, respectively.Then, m lines follow. The i-th of them contains three integers x_i,y_i,z_i (1<=x_i,y_i<=n; x_iney_i; 0<=z_i<=10^5) — the description of the i-th operation.The next line contains one integer q (1<=q<=1000) — the number of queries.Each query consists of two lines:  the first line contains one integer k (0<=k<=10^9) — the maximum number of times you can choose a variable and decrease it by 1;  the second line contains n integers a_1,a_2,...,a_n (0<=a_i<=10^9) — the initial values of the variables. OutputFor each query, print a string of n zeroes and/or ones. The i-th character should be 1 if it is possible to obtain an i-unstable sequence, or 0 otherwise.ExamplesInput4 52 1 103 2 51 4 81 2 63 1 173020 0 15 51020 0 15 53020 0 15 5Output0000
0000
0110
Input3 51 2 1001 2 101 3 51 2 1003 2 5110000000000 0 0Output000
Input3 42 3 51 2 03 1 41 3 41057 5 325 7 011 1 153 0 105 3 556 0 451 5 617 7 211 6 647 7 2Output000
000
000
001
000
001
001
000
000
000
NoteConsider the first example. If the initial variable values are [20,0,15,5], the resulting values will be [6,0,5,5] with any order of operations. Decreasing the variables 10 times is not enough. However, if we can apply no more than 30 changes, we can decrease the 1-st variable by 2, and the 4-th variable by 25, we get initial values equal to [18,0,15,-20], and this sequence is 2-unstable and 3-unstable:  if you apply the operations in the order they are given, you will get [-12,0,5,-20];  however, if you apply the operations in order [3,2,4,1,5], you will get [-12,-2,5,-20];  and if you apply the operations in order [3,4,5,1,2], you will get [-12,-2,3,-20].. Output only the code with no comments, explanation, or additional text.