P10733 [NOISG 2019 Prelim] Lost Array

Translated from [NOISG2019 Prelim B.Lost Array](https://github.com/noisg/sg_noi_archive/blob/master/2019_prelim/). **This problem uses Special Judge. Any answer that satisfies the conditions will be considered correct.**

Given $M$ relations of the form $\min (X_{A_i}, X_{B_i}) = C_i$, construct an array $X$ of length $N$ such that every number in the array is between $1$ and $10^9$, and the array satisfies all relations. It is guaranteed that such an array exists.

The first line contains two integers $N, M$. The next $M$ lines each contain three numbers $A_i, B_i, C_i$.

Output one line with $N$ integers, representing the array $X$ you construct.

### Sample #1 Explanation Clearly, $\min (X_2, X_1) = \min (9, 7) = 7$, which satisfies the conditions. ### Sample #3 Explanation The original statement did not include this sample, but it exists in the testdata. The first constraint is $\min (X_1, X_2) = 1$. In fact, all constraints are the same as this one. ### Sample #4 Explanation The only constraint is $\min (X_1, X_2) = 123$. The other numbers can be any values between $1$ and $10^9$. ### Constraints | $\text{Subtask}$ | Score | Special Property | | :----------: | :----------: | :----------: | | $0$ | $0$ | Samples | | $1$ | $5$ | $N = 2, M = 1$ | | $2$ | $6$ | $M \leq 3$ | | $3$ | $20$ | $N, M \leq 1000$ | | $4$ | $21$ | $C_i \leq 10, N \leq 5$ | | $5$ | $48$ | None | For $100\%$ of the data: - $1 \leq N, M \leq 10^5$. - $1 \leq A_i, B_i \leq N$. - $A_i \neq B_i$. - $1 \leq C_i \leq 10^9$. Translated by ChatGPT 5