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 <stdio.h>
#include <queue>
#include <utility>
#include <vector>
using namespace std;
typedef pair<int,int> pi;
#define F first
#define S second
#define MP make_pair
#define PB push_back
const int N=1e5+10;
const int INF=1e9+10;
int main(){
int n,m,s,d[N],l;
pi temp,nxt;
vector<pi> graph[N];
priority_queue<pi,vector<pi>,greater<pi>>pq;
scanf("%d%d%d",&n,&m,&s);
for(int i=0;i<n;i++)d[i]=INF;
d[s]=0;
while(m--){
scanf("%d%d%d",&l,&temp.F,&temp.S);
graph[l].PB(temp);
}
pq.push(MP(0,s));
while(!pq.empty()){
nxt=pq.top();
pq.pop();
if(d[nxt.S]<nxt.F)continue;
for(int i=0;i<graph[nxt.S].size();i++)if(nxt.F+graph[nxt.S][i].S<d[graph[nxt.S][i].F]){
d[graph[nxt.S][i].F]=nxt.F+graph[nxt.S][i].S;
pq.push(MP(d[graph[nxt.S][i].F],graph[nxt.S][i].F));
}
}

for(int i=0;i<n;i++)if(d[i]==INF)printf("INF\n");
else printf("%d\n",d[i]);
}