Problem:
Score: 600 points

Problem Statement

M-kun is a brilliant air traffic controller.

On the display of his radar, there are N airplanes numbered 1, 2, ..., N, all flying at the same altitude.

Each of the airplanes flies at a constant speed of 0.1 per second in a constant direction. The current coordinates of the airplane numbered i are (X_i, Y_i), and the direction of the airplane is as follows:

if U_i is U, it flies in the positive y direction;

if U_i is R, it flies in the positive x direction;

if U_i is D, it flies in the negative y direction;

if U_i is L, it flies in the negative x direction.

To help M-kun in his work, determine whether there is a pair of airplanes that will collide with each other if they keep flying as they are now.

If there is such a pair, find the number of seconds after which the first collision will happen.

We assume that the airplanes are negligibly small so that two airplanes only collide when they reach the same coordinates simultaneously.

Constraints

1 \leq N \leq 200000

0 \leq X_i, Y_i \leq 200000

U_i is U, R, D, or L.

The current positions of the N airplanes, (X_i, Y_i), are all distinct.

N, X_i, and Y_i are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 Y_1 U_1
X_2 Y_2 U_2
X_3 Y_3 U_3
:
X_N Y_N U_N

Output

If there is a pair of airplanes that will collide with each other if they keep flying as they are now, print an integer representing the number of seconds after which the first collision will happen.

If there is no such pair, print SAFE.

Sample Input 1

2
11 1 U
11 47 D

Sample Output 1

230

If the airplanes keep flying as they are now, two airplanes numbered 1 and 2 will reach the coordinates (11, 24) simultaneously and collide.

Sample Input 2

4
20 30 U
30 20 R
20 10 D
10 20 L

Sample Output 2

SAFE

No pair of airplanes will collide.

Sample Input 3

8
168 224 U
130 175 R
111 198 D
121 188 L
201 116 U
112 121 R
145 239 D
185 107 L

Sample Output 3

100

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {

    public static void main(String[] args) throws IOException {
        new Main().solve();
    }

    private void solve() throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        int n = Integer.parseInt(f.readLine());
        TreeSet<Plane> up = new TreeSet<Plane>(new DownUp());
        TreeSet<Plane> down = new TreeSet<Plane>(new DownUp());
        TreeSet<Plane> right = new TreeSet<Plane>(new PlaneComparator());
        TreeSet<Plane> left = new TreeSet<Plane>(new PlaneComparator());
        for (int i = 0; i < n; i++) {
            StringTokenizer tokenizer = new StringTokenizer(f.readLine());
            int x = Integer.parseInt(tokenizer.nextToken());
            int y = Integer.parseInt(tokenizer.nextToken());
            char dir = tokenizer.nextToken().charAt(0);
            if (dir == 'U') up.add(new Plane(x, y));
            if (dir == 'D') down.add(new Plane(x, y));
            if (dir == 'R') right.add(new Plane(x, y));
            if (dir == 'L') left.add(new Plane(x, y));
        }


        int min = Integer.MAX_VALUE;
        for (Plane upPlane : up) {
            if (!right.isEmpty()) {
                Plane rightPlane = right.floor(upPlane);
                //System.out.println(upPlane + " " + rightPlane);
                if (rightPlane != null && rightPlane.n == upPlane.n && rightPlane.x < upPlane.x) {
                    min = Math.min(min, upPlane.x - rightPlane.x);
                }
            }
            if (!left.isEmpty()) {
                Plane leftPlane = left.ceiling(upPlane);
                //System.out.println(upPlane + " " + leftPlane);
                if (leftPlane != null && leftPlane.n == upPlane.n && leftPlane.x > upPlane.x) {
                    min = Math.min(min, leftPlane.x - upPlane.x);
                }
            }
        }
        for (Plane downPlane : down) {
            if (!right.isEmpty()) {
                Plane rightPlane = right.floor(downPlane);
                //System.out.println(downPlane + " " + rightPlane);
                if (rightPlane != null && rightPlane.n == downPlane.n && rightPlane.x < downPlane.x) {
                    min = Math.min(min, downPlane.x - rightPlane.x);
                }
            }
            if (!left.isEmpty()) {
                Plane leftPlane = left.ceiling(downPlane);
                //System.out.println(downPlane + " " + leftPlane);
                if (leftPlane != null && leftPlane.n == downPlane.n && leftPlane.x > downPlane.x) {
                    min = Math.min(min, leftPlane.x - downPlane.x);
                }
            }
        }


        TreeSet<Plane>[] up1 = new TreeSet[2];
        TreeSet<Plane>[] down1 = new TreeSet[2];
        for (int i = 0; i < 2; i++) {
            up1[i] = new TreeSet<Plane>(new DownUp());
            down1[i] = new TreeSet<Plane>(new DownUp());
        }
        for (Plane plane : up) {
            up1[plane.y % 2].add(plane);
        }
        for (Plane plane : down) {
            down1[plane.y % 2].add(plane);
        }

        for (int i = 0; i < 2; i++) {
            for (Plane planeUp : up1[i]) {
                Plane planeDown = down1[i].ceiling(planeUp);
                if (planeDown == null) continue;
                if (planeDown.x == planeUp.x) {
                    min = Math.min((planeDown.y - planeUp.y) / 2, min);
                }
            }
        }


        if (min == Integer.MAX_VALUE) {
            out.println("SAFE");
        } else {
            out.println(min * 10);
        }
        out.close();
    }

    private static class Plane {
        int x;
        int y;
        int n;

        @Override
        public String toString() {
            return "Plane{" +
                    "x=" + x +
                    ", y=" + y +
                    ", n=" + n +
                    '}';
        }

        public Plane(int x, int y) {
            this.x = x;
            this.y = y;
            n = x + y;
        }
    }

    private static class DownUp implements Comparator<Plane> {

        @Override
        public int compare(Plane o1, Plane o2) {
            int compareX =  Integer.compare(o1.x, o2.x);
            if (compareX != 0) return compareX;
            return Integer.compare(o1.y, o2.y);
        }
    }

    private static class PlaneComparator implements Comparator<Plane> {

        @Override
        public int compare(Plane o1, Plane o2) {
            if (o1.n < o2.n) return -1;
            if (o1.n > o2.n) return 1;
            return Integer.compare(o1.x, o2.x);
        }
    }
}