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;

const int INF = 1e9;

int main() {
	int V, E, r;
	cin >> V >> E >> r;
	vector<vector<pair<int, int>>> G(V, vector<pair<int, int>>());
	for (int i=0;i<E;i++) {
		int s, t, d;
		cin >> s >> t >> d;
		pair<int, int> p = make_pair(t, d);
		G[s].push_back(p);
	}

	vector<int> cost(V, -1);
	priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
	pair<int, int> first = make_pair(0, r); // first: cost, second: vertex
	pq.push(first);
	while (!pq.empty()) {
		pair<int, int> rem = pq.top();
		pq.pop();
		if (cost[rem.second] != -1) continue;
		cost[rem.second] = rem.first;
		for (pair<int, int> p : G[rem.second]) {
			if (cost[p.first] == -1) {
				pair<int, int> tmp = make_pair(rem.first+p.second, p.first);
				pq.push(tmp);
			}
		}
	}

	for (int i=0;i<V;i++) {
		if (cost[i] == -1) {
			cout << "INF" << endl;
		} else {
			cout << cost[i] << endl;
		}
	}
}