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<iostream>
#include<vector>
#include<queue>
#include<algorithm>
#include<functional>
using namespace std;
typedef pair<int, int> pii;

const int INF = 1e9;
const int MAX_V = 100000;

int V, E, r;
vector<pii> G[MAX_V];
int d[MAX_V];

void dijkstra(int s) {
	priority_queue<pii, vector<pii>, greater<pii> > que;
	for (int i = 0; i < V; i++) d[i] = INF;
	d[s] = 0;
	que.push(make_pair(0, s));

	while (!que.empty()) {
		pii p = que.top();
		que.pop();
		int v = p.second;
		if (d[v] < p.first) continue;
		for (int i = 0; i < G[v].size(); i++) {
			pii e = G[v][i];
			if (d[e.first] > d[v] + e.second) {
				d[e.first] = d[v] + e.second;
				que.push(make_pair(d[e.first], e.first));
			}
		}
	}
}

int main() {
	cin >> V >> E >> r;
	for (int i = 0; i < E; i++) {
		int a, b, c;
		cin >> a >> b >> c;
		G[a].push_back(make_pair(b, c));
	}
	dijkstra(r);
	for (int i = 0; i < V; i++) {
		if (d[i] == INF) {
			cout << "INF" << endl;
			continue;
		}
		cout << d[i] << endl;
	}
}