Problem: For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Constraints

* 1 ≤ |V| ≤ 100000
* 0 ≤ di ≤ 10000
* 0 ≤ |E| ≤ 500000
* There are no parallel edges
* There are no self-loops

Input

An edge-weighted graph G (V, E) and the source r.


|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1


|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

Print the costs of SSSP in the following format.


c0
c1
:
c|V|-1


The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF.

Examples

Input

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5


Output

0
1
3
4


Input

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5


Output

3
0
2
INF

Solution (in CPP):

Solution:
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<queue>
using namespace std;
const int INF=2147483647;
const int maxn=100000;
const int maxm=500000;
int n,m,s;
int fir[maxn],nxt[maxm],to[maxm],val[maxm],cnt;
void add_edge(int u,int v,int w)
{
    nxt[++cnt]=fir[u];fir[u]=cnt;to[cnt]=v;val[cnt]=w;
}
int dis[maxn],inq[maxn];
void SPFA(int s)
{
    for(int i=0;i<n;i++) dis[i]=INF; dis[s]=0;
    queue<int>Q;Q.push(s);
    while(!Q.empty()) {
        int u=Q.front(); Q.pop();
        for(int e=fir[u];e;e=nxt[e]) {
            int v=to[e],w=val[e];
            if(dis[u]+w<dis[v]) {
                dis[v]=dis[u]+w;
                if(!inq[v]) Q.push(v);
            }
        }
    }
}
int main()
{
    scanf("%d%d%d",&n,&m,&s);
    for(int u,v,w,i=0;i<m;i++) {
        scanf("%d%d%d",&u,&v,&w);
        add_edge(u,v,w);
    }
    SPFA(s);
    for(int i=0;i<n;i++){
	if (dis[i] == INF) {
		printf("INF\n");
	}else{
		printf("%d\n",dis[i]);
	}
}
    return 0;
}