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>
#include <array>
using namespace std;
using ULL = unsigned long long;
using UL = unsigned;
using LL = long long;
#define rep(i, n) for(UL i = 0; i < (n); i++)

struct Problem {

	void Solve() {
		UL V, E, r; cin >> V >> E >> r;
		vector<vector<pair<UL, UL>>> G(V);
		rep(i, E) {
			UL a, b, d; cin >> a >> b >> d;
			G[a].push_back({ b, d });
		}
		priority_queue<pair<UL, UL>, vector<pair<UL, UL>>, greater<pair<UL, UL>>> Q;
		Q.push({ 0, r });
		vector<UL> ans(V, (UL) -1);
		while (Q.size()) {
			pair<UL, UL> p = Q.top(); Q.pop();
			if (ans[p.second] != (UL)-1) continue;
			ans[p.second] = p.first;
			for (auto e : G[p.second]) {
				Q.push({ p.first + e.second, e.first });
			}
		}
		rep(i, V) {
			if (ans[i] == (UL)-1) cout << "INF" << endl;
			else cout << ans[i] << endl;
		}
	}


	Problem();
};
int main() {
	unique_ptr<Problem> p(new Problem());
	p->Solve();
	return 0;
}
Problem::Problem() {
	cout << fixed << setprecision(10);
}