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 fi first
#define se second
#define pb push_back
#define mp make_pair
using namespace std;
typedef pair <int, int> pii;

const int INF = 0x3f3f3f3f;
int n, m, r, t1, t2, t3, d[100005];
pii p1;
vector <pii> v[100005];
priority_queue <pii, vector <pii>, greater <pii>> q;

int main() {
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	cin >> n >> m >> r;
	for (int i = 0; i < n; i++) d[i] = INF;
	for (int i = 0; i < m; i++) {
		cin >> t1 >> t2 >> t3;
		v[t1].pb(mp(t2, t3));
//		v[t2].pb(mp(t1, t3));
	}
	d[r] = 0;
	q.push(mp(0, r));
	while (!q.empty()) {
		p1 = q.top(); q.pop();
		int &w = p1.fi, &u = p1.se;
		if (d[u] != w) continue;
		for (pii i : v[u]) {
			if (w + i.se < d[i.fi]) {
				d[i.fi] = w + i.se;
				q.push(mp(d[i.fi], i.fi));
			}
		}
	}
	for (int i = 0; i < n; i++) {
		if (d[i] == INF) cout << "INF" << endl;
		else cout << d[i] << endl;
	}
}