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 <bits/stdc++.h>
#define pb push_back
using namespace std;
const int INF=0x3f3f3f3f;
const int maxn=100005;

struct edge{int to,cost;};

int n,m,s;
int d[maxn];
int qh,qt,q[maxn];
bool ok=1,inq[maxn];
vector<edge>G[maxn];

int main() {
	cin>>n>>m>>s;
	for (int i=0;i<m;i++) {
		int u,v,w; cin>>u>>v>>w;
		G[u].pb(edge{v,w});
	}
	memset(d,0x3f,sizeof(d));
	d[s]=0;
	q[qt++]=s; inq[s]=1;
	while (qh!=qt) {
		int u=q[qh++]; if (qh>=maxn) qh=0;
		inq[u]=0;
		for (edge e:G[u]) {
			if (d[e.to]>d[u]+e.cost) {
				d[e.to]=d[u]+e.cost;
				if (!inq[e.to]) {
					q[qt++]=e.to; if (qt>=maxn) qt=0;
					inq[e.to]=1;
				}
			}
		}
	}
    for (int i=0;i<n;i++) 
		if (d[i]==INF) cout<<"INF"<<'\n';
		else cout<<d[i]<<'\n';
}