P7887 "MCOI-06" Existence of Truth

There may exist a sequence of non-negative integers $a_1,a_2,\dots,a_n$ such that $0\le a_i

**This problem contains multiple test cases.** The first line contains a positive integer $T$, representing the number of test cases. For each test case: The first line contains a positive integer $n$. The next $n$ lines each contain three positive integers $x_i,y_i,z_i$.

For each test case, output in order: The first line contains a non-negative integer $k$, the number of valid solutions. If $k=1$, output $n$ non-negative integers on the second line, in order: $a_1,a_2,\dots,a_n$.

#### Constraints and Notes **This problem uses bundled testdata.** - Subtask 1 (10 pts): $n=1$. - Subtask 2 (19 pts): $\sum n\le100$. - Subtask 3 (19 pts): $x_i=y_i=1$. - Subtask 4 (22 pts): It is guaranteed that there is a **unique solution.** - Subtask 5 (30 pts): No special restrictions. For all testdata: - $1\le n,\sum n\le 2\times10^5$; - $1\le x_i,y_i