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 ff first
#define ss second
#define pb push_back
using namespace std;
typedef long long ll;
const ll INF=0x3f3f3f3f3f3f3f3f;

ll d[100005];
int n,m,r;
vector<pair<ll,int>>G[100005];
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>>pq;

int main() {
	cin>>n>>m>>r;
	for (int i=0;i<n;i++) d[i]=INF;
	for (int i=0;i<m;i++) {
		int s,t; ll w; cin>>s>>t>>w;
		G[s].pb({w,t});
	}
	d[r]=0;
	pq.push({0,r});
	while (pq.size()) {
		ll dis=pq.top().ff;
		int v=pq.top().ss;
		pq.pop();
		if (d[v]<dis) continue;
		for (auto p:G[v]) {
			if (dis+p.ff<d[p.ss]) {
				d[p.ss]=dis+p.ff;
				pq.push({d[p.ss],p.ss});
			}
		}
	}
	for (int i=0;i<n;i++) {
		if (d[i]==INF) cout<<"INF";
		else cout<<d[i];
		cout<<'\n';
	}
}