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.

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.

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.

Sample Input 1

4 4
1 2 5
2 3 10
3 1 15
4 3 20

Sample Output 1

30
30
30
-1

By Roads 1, 2, 3, Towns 1, 2, 3 forms a ring that takes 30 minutes to go around.
From Town 4, we can go to Towns 1, 2, 3, but then we cannot return to Town 4.

Sample Input 2

4 6
1 2 5
1 3 10
2 4 5
3 4 10
4 1 10
1 1 10

Sample Output 2

10
20
30
20

There may be a road such that A_i = B_i.
Here, we can use just Road 6 to depart from Town 1 and return to that town.

Sample Input 3

4 7
1 2 10
2 3 30
1 4 15
3 4 25
3 4 20
4 3 20
4 3 30

Sample Output 3

-1
-1
40
40

Note that there may be multiple roads connecting the same pair of towns.

见题面 Input 部分

见题面 Output 部分