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>
using namespace std;
#define ll long long
int n,m,s;
struct point{
	int v;
	ll w;
	bool operator<(const point&p)const{
		return w>p.w;
	}
};
ll d[100005];
bool vis[1000005];
ll inf=1e12;
vector<point>e[100005];
void solve(){
	fill(d,d+n+1,inf);
	d[s]=0;vis[s]=1;
	priority_queue<point> q;
	for(int i=0;i<e[s].size();i++)q.push(e[s][i]);
	int k=1;
	while(k!=n&&!q.empty()){
		point p=q.top();q.pop();
		if(!vis[p.v]){
			d[p.v]=p.w;
			vis[p.v]=1;
			for(int i=0;i<e[p.v].size();i++)q.push({e[p.v][i].v,e[p.v][i].w+p.w});
			k++;
		}		
	}
	for(int i=0;i<n;i++){
		if(d[i]>=inf){
			cout<<"INF"<<endl;
		}else cout<<d[i]<<endl;
	}
}
int main(){
	cin>>n>>m>>s;
	int u,v,w;
	while(m--){
		cin>>u>>v>>w;
		e[u].push_back({v,w});
	}
	solve();
	return 0;
}