D. 2+ doors
time limit per test
1.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The Narrator has an integer array $a$ of length $n$, but he will only tell you the size $n$ and $q$ statements, each of them being three integers $i, j, x$, which means that $a_i \mid a_j = x$, where $|$ denotes the bitwise OR operation.

Find the lexicographically smallest array $a$ that satisfies all the statements.

An array $a$ is lexicographically smaller than an array $b$ of the same length if and only if the following holds:

• in the first position where $a$ and $b$ differ, the array $a$ has a smaller element than the corresponding element in $b$.
Input

In the first line you are given with two integers $n$ and $q$ ($1 \le n \le 10^5$, $0 \le q \le 2 \cdot 10^5$).

In the next $q$ lines you are given with three integers $i$, $j$, and $x$ ($1 \le i, j \le n$, $0 \le x < 2^{30}$) — the statements.

It is guaranteed that all $q$ statements hold for at least one array.

Output

On a single line print $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i < 2^{30}$) — array $a$.

Examples
Input
4 3
1 2 3
1 3 2
4 1 2

Output
0 3 2 2
Input
1 0

Output
0
Input
2 1
1 1 1073741823

Output
1073741823 0
Note

In the first sample, these are all the arrays satisfying the statements:

• $[0, 3, 2, 2]$,
• $[2, 1, 0, 0]$,
• $[2, 1, 0, 2]$,
• $[2, 1, 2, 0]$,
• $[2, 1, 2, 2]$,
• $[2, 3, 0, 0]$,
• $[2, 3, 0, 2]$,
• $[2, 3, 2, 0]$,
• $[2, 3, 2, 2]$.