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 int long long
#define INF INT_MAX
#define P pair<int,int>
using namespace std;

int d[100000];
vector<P>f[500000]{};
signed main(){
int a,b,c;
cin>>a>>b>>c;
fill(d,d+a+1,INF);
d[c]=0;
priority_queue<P,vector<P>,greater<P>>Q;
Q.push(P(0,c));
for(int h=0;h<b;h++){
int i,j,k;
scanf("%lld%lld%lld",&i,&j,&k);
f[i].push_back(P(k,j));
}
while(Q.empty()==false){
P o=Q.top();
Q.pop();
int u=o.second;
if(d[u]<o.first)continue;
for(int x=0;x<f[u].size();x++){
P l=f[u][x];
if(d[l.second]>d[u]+l.first){
d[l.second]=d[u]+l.first;
Q.push(P(d[l.second],l.second));
}
}
}
for(int y=0;y<a;y++){
if(d[y]!=INF) printf("%lld\n",d[y]);
else printf("INF\n");
}
}