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 mod 10000000070
#define for0(i, n) for(int i = 0; i < (n); i++)
#define mp make_pair
#define puts(x) cout << x << endl
using namespace std;
int v, e, r, ans[123456];
typedef pair<int, int> P;
vector<P>g[123456];
priority_queue<P, vector<P>, greater<P>>pq;
signed main() {
	cin >> v >> e >> r;
	for0(i, v)ans[i] = mod;
	while (e--) {
		int s, t, d; cin >> s >> t >> d;
		g[s].push_back(mp(t, d));
	}
	pq.push(mp(0, r));
	while (pq.size()) {
		P p1 = pq.top(); pq.pop();
		if (ans[p1.second] != mod)continue;
		ans[p1.second] = p1.first;
		for (P pv : g[p1.second]) {
			if (ans[pv.first] == mod)pq.push(mp(ans[p1.second] + pv.second, pv.first));
		}
	}
	for0(i, v)
		if (ans[i] == mod)puts("INF");
		else puts(ans[i]);
}