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CSES Problem Set

Shortest Routes I


Task | Statistics


CSES - Shortest Routes ICSES - Shortest Routes I

Time limit:1.00 s Memory limit:512 MB

There are $n$ cities and $m$ flight connections between them. Your task is to determine the length of the shortest route from Syrjälä to every city.

Input

The first input line has two integers $n$ and $m$: the number of cities and flight connections. The cities are numbered $1,2,\dots,n$, and city $1$ is Syrjälä.

After that, there are $m$ lines describing the flight connections. Each line has three integers $a$, $b$ and $c$: a flight begins at city $a$, ends at city $b$, and its price is $c$. Each flight is a one-way flight.

You can assume that it is possible to travel from Syrjälä to all other cities.

Output

Print $n$ integers: the shortest route lengths from Syrjälä to cities $1,2,\dots,n$.

Constraints
Example

Input:
3 4
1 2 6
1 3 2
3 2 3
1 3 4


Output:
0 5 2