Problem: Vasya has a graph containing both directed (oriented) and undirected (non-oriented) edges. There can be multiple edges between a pair of vertices.

Vasya has picked a vertex s from the graph. Now Vasya wants to create two separate plans:

  1. to orient each undirected edge in one of two possible directions to maximize number of vertices reachable from vertex s; 
  2. to orient each undirected edge in one of two possible directions to minimize number of vertices reachable from vertex s. 



In each of two plans each undirected edge must become directed. For an edge chosen directions can differ in two plans.

Help Vasya find the plans.

Input

The first line contains three integers n, m and s (2 ≤ n ≤ 3·105, 1 ≤ m ≤ 3·105, 1 ≤ s ≤ n) — number of vertices and edges in the graph, and the vertex Vasya has picked.

The following m lines contain information about the graph edges. Each line contains three integers ti, ui and vi (1 ≤ ti ≤ 2, 1 ≤ ui, vi ≤ n, ui ≠ vi) — edge type and vertices connected by the edge. If ti = 1 then the edge is directed and goes from the vertex ui to the vertex vi. If ti = 2 then the edge is undirected and it connects the vertices ui and vi.

It is guaranteed that there is at least one undirected edge in the graph.

Output

The first two lines should describe the plan which maximizes the number of reachable vertices. The lines three and four should describe the plan which minimizes the number of reachable vertices.

A description of each plan should start with a line containing the number of reachable vertices. The second line of a plan should consist of f symbols '+' and '-', where f is the number of undirected edges in the initial graph. Print '+' as the j-th symbol of the string if the j-th undirected edge (u, v) from the input should be oriented from u to v. Print '-' to signify the opposite direction (from v to u). Consider undirected edges to be numbered in the same order they are given in the input.

If there are multiple solutions, print any of them.

Examples

Input

2 2 1
1 1 2
2 2 1


Output

2
-
2
+


Input

6 6 3
2 2 6
1 4 5
2 3 4
1 4 1
1 3 1
2 2 3


Output

6
++-
2
+-+

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(in, out);
        out.close();
    }

    static class TaskC {

        public class UndirectedEdge {
            Node u, v;
            int direction = -1;
            boolean ub = false, vb = false;

            public UndirectedEdge(Node u, Node v) {
                this.u = u;
                this.v = v;
            }

        }

        public class Node {
            boolean visited = false;
            HashSet<Node> e = new HashSet<>();
            ArrayList<UndirectedEdge> eu = new ArrayList<>();

        }

        public void solve(InputReader in, PrintWriter out) {
            int n = in.NextInt();
            int m = in.NextInt();
            int s = in.NextInt() - 1;
            Node[] nodes = new Node[n];
            ArrayList<UndirectedEdge> undirectedEdges = new ArrayList<>();
            for (int i = 0; i < n; i++) nodes[i] = new Node();
            for (; m > 0; m--) {
                int t = in.NextInt();
                int u = in.NextInt() - 1;
                int v = in.NextInt() - 1;
                if (t == 1) {
                    nodes[u].e.add(nodes[v]);
                } else {
                    UndirectedEdge e = new UndirectedEdge(nodes[u], nodes[v]);
                    nodes[u].eu.add(e);
                    nodes[v].eu.add(e);
                    undirectedEdges.add(e);
                }
            }
            Set<UndirectedEdge> q = new HashSet<>();
            Queue<Node> qn = new LinkedList<>();
            qn.add(nodes[s]);
            int count = 0;
            do {
                for (UndirectedEdge e : q) {
                    if (e.ub) e.direction = 0;
                    else e.direction = 1;
                    qn.add(e.v);
                    qn.add(e.u);
                }
                q.clear();
                while (qn.isEmpty() == false) {
                    Node nn = qn.poll();
                    if (nn.visited) continue;
                    nn.visited = true;
                    count++;
                    qn.addAll(nn.e);
                    for (UndirectedEdge ue : nn.eu) {
                        if (ue.direction != -1) continue;
                        ue.vb |= ue.v == nn;
                        ue.ub |= ue.u == nn;
                        q.add(ue);
                    }
                }
            } while (q.isEmpty() == false);
            out.println(count);
            for (UndirectedEdge ue : undirectedEdges) {
                out.print((ue.direction == 1 ? "-" : "+"));
            }
            out.println();

            qn.add(nodes[s]);
            q.clear();
            for (UndirectedEdge e : undirectedEdges) e.direction = -1;
            for (Node nn : nodes) nn.visited = false;
            count = 0;
            do {
                for (UndirectedEdge e : q) {
                    if (e.ub) e.direction = 1;
                    else e.direction = 0;
                }
                q.clear();
                while (qn.isEmpty() == false) {
                    Node nn = qn.poll();
                    if (nn.visited) continue;
                    nn.visited = true;
                    count++;
                    qn.addAll(nn.e);
                    for (UndirectedEdge ue : nn.eu) {
                        if (ue.direction != -1) continue;
                        ue.vb |= ue.v == nn;
                        ue.ub |= ue.u == nn;
                        q.add(ue);
                    }
                }
            } while (q.isEmpty() == false);
            out.println(count);
            for (UndirectedEdge ue : undirectedEdges) {
                out.print((ue.direction == 1 ? "-" : "+"));
            }
            out.println();
        }
    }

    public static int GetMax(int[] ar) {
        int max = Integer.MIN_VALUE;
        for (int a : ar) {
            max = Math.max(max, a);
        }
        return max;
    }

    public static int GetMin(int[] ar) {
        int min = Integer.MAX_VALUE;
        for (int a : ar) {
            min = Math.min(min, a);
        }
        return min;
    }

    public static int[] GetCount(int[] ar) {
        return GetCount(ar, GetMax(ar));
    }

    public static int[] GetCount(int[] ar, int maxValue) {
        int[] dp = new int[maxValue + 1];
        for (int a : ar) {
            dp[a]++;
        }
        return dp;
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String Next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int NextInt() {
            return Integer.parseInt(Next());
        }

        public long NextLong() {
            return Long.parseLong(Next());
        }

        public double NextDouble() {
            return Double.parseDouble(Next());
        }

        public int[] NextIntArray(int n) {
            return NextIntArray(n, 0);
        }

        public int[] NextIntArray(int n, int offset) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = NextInt() - offset;
            }
            return a;
        }

        public int[][] NextIntMatrix(int n, int m) {
            return NextIntMatrix(n, m, 0);
        }

        public int[][] NextIntMatrix(int n, int m, int offset) {
            int[][] a = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    a[i][j] = NextInt() - offset;
                }
            }
            return a;
        }
    }
}