Problem Statement

In the Republic of AtCoder, there are $N$ towns numbered $1$ through $N$ and $M$ roads numbered $1$ through $M$. Road $i$ is a one-way road from Town $A_i$ to Town $B_i$, and it takes $C_i$ minutes to go through. It is possible that $A_i = B_i$, and there may be multiple roads connecting the same pair of towns. Takahashi is thinking about taking a walk in the country. We will call a walk valid when it goes through one or more roads and returns to the town it starts at. For each town, determine whether there is a valid walk that starts at that town. Additionally, if the answer is yes, find the minimum time such a walk requires.

Constraints

• $1 \le N \le 2000$
• $1 \le M \le 2000$
• $1 \le A_i \le N$
• $1 \le B_i \le N$
• $1 \le C_i \le 10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1 C_1
A_2 B_2 C_2
A_3 B_3 C_3
\hspace{25pt} \vdots
A_M B_M C_M

Output

Print $N$ lines. The $i$-th line $(1 \le i \le N)$ should contain the following:

• if there is a valid walk that starts at Town $i$, the minimum time required by such a walk;
• otherwise, -1.