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 JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.util.*;

public class Main {
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int v = sc.nextInt();
		int e = sc.nextInt();
		int r = sc.nextInt();
		int[] s = new int[e];
		int[] t = new int[e];
		int[] d = new int[e];
		for (int i = 0; i < e; i++) {
			s[i] = sc.nextInt();
			t[i] = sc.nextInt();
			d[i] = sc.nextInt();
		}
		new Dijkstra(v, e, r, s, t, d).ans();
	}
}

class Dijkstra {
	static class Edge {
		int from;
		int to;
		int cost;
		Edge(int from, int to, int cost) {
			this.from = from;
			this.to = to;
			this.cost = cost;
		}
	}
	static class Node {
		int num;
		int cost;
		Node(int num, int cost) {
			this.num = num;
			this.cost = cost;
		}
	}
	static final int INF = Integer.MAX_VALUE;
	int v;
	int e;
	int r;
	int[] distance;
	TreeMap<Integer, ArrayList<Edge>> map;
	public Dijkstra(int v, int e, int r, int[] s, int[] t, int[] d) {
		this.v = v;
		this.e = e;
		this.r = r;
		map = new TreeMap<>();
		for (int i = 0; i < v; i++) {
			map.put(i, new ArrayList<>());
		}
		for (int i = 0; i < e; i++) {
			map.get(s[i]).add(new Edge(s[i], t[i], d[i]));
		}
	}
	void run() {
		distance = new int[v];
		for (int i = 0; i < v; i++) {
			if (i != r) {
				distance[i] = INF;
			}
		}
		PriorityQueue<Node> queue = new PriorityQueue<>(Comparator.comparingInt(o -> o.cost));
		for (int i = 0; i < v; i++) {
			queue.add(new Node(i, distance[i]));
		}
		while (!queue.isEmpty()) {
			Node node = queue.poll();
			if (node.cost != distance[node.num]) {
				continue;
			}
			for (Edge edge: map.get(node.num)) {
				if (distance[edge.from] == INF) {
					continue;
				}
				if (distance[edge.to] > distance[edge.from] + edge.cost) {
					distance[edge.to] = distance[edge.from] + edge.cost;
					queue.add(new Node(edge.to, distance[edge.to]));
				}
			}
		}
	}
	public void ans() {
		run();
		for (int i = 0; i < v; i++) {
			if (distance[i] == INF) {
				System.out.println("INF");
			} else {
				System.out.println(distance[i]);
			}
		}
	}
}





class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() {
		if (hasNextByte()) {
			return buffer[ptr++];
		} else {
			return -1;
		}
	}
	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}
	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
			ptr++;
		}
		return hasNextByte();
	}
	public String next() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || Integer.MAX_VALUE < nl) {
			throw new NumberFormatException();
		}
		return (int) nl;
	}
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}