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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.IO;
using System.Text;
using System.Linq;

using E = System.Linq.Enumerable;
using System.Runtime.InteropServices.ComTypes;
using System.Data.SqlTypes;
using System.Numerics;

internal partial class Solver {

    public int[] dx = new int[] { 0, 1, 0, -1 };
    public int[] dy = new int[] { 1, 0, -1, 0 };
    public string ds = "URDL";

    public void Run() {
        var n = ni();
        var x = new int[n];
        var y = new int[n];
        var u = new char[n];
        for (int i = 0; i < n; i++) {
            x[i] = ni();
            y[i] = ni();
            u[i] = ns()[0];
        }

        long ans = long.MaxValue;

        for (int k = 0; k < 4; k++) {
            var perm = E.Range(0, n)
                .OrderBy(i => x[i])
                .ToArray();

            var rdGroup = perm
                .Where(i => u[i] == 'R' || u[i] == 'D')
                .GroupBy(i => x[i] - y[i])
                .ToArray();

            foreach (var g in rdGroup) {
                var a = g.ToArray();
                for (int i = 0; i + 1 < a.Length; i++) {
                    var p1 = a[i];
                    var p2 = a[i + 1];
                    if (u[p1] == 'R' && u[p2] == 'D') {
                        ans = Math.Min(ans, (x[p2] - x[p1]) * 10);
                    }
                }
            }

            var ruGroup = perm
                .Where(i => u[i] == 'R' || u[i] == 'U')
                .GroupBy(i => x[i] + y[i])
                .ToArray();

            foreach (var g in ruGroup) {
                var a = g.ToArray();
                for (int i = 0; i + 1 < a.Length; i++) {
                    var p1 = a[i];
                    var p2 = a[i + 1];
                    if (u[p1] == 'R' && u[p2] == 'U') {
                        ans = Math.Min(ans, (x[p2] - x[p1]) * 10);
                    }
                }
            }

            var rlGroup = perm
                .Where(i => u[i] == 'R' || u[i] == 'L')
                .GroupBy(i => y[i])
                .ToArray();

            foreach (var g in rlGroup) {
                var a = g.ToArray();
                for (int i = 0; i + 1 < a.Length; i++) {
                    var p1 = a[i];
                    var p2 = a[i + 1];
                    if (u[p1] == 'R' && u[p2] == 'L') {
                        ans = Math.Min(ans, (x[p2] - x[p1]) * 5);
                    }
                }
            }

            for (int i = 0; i < n; i++) {
                (x[i], y[i]) = (-y[i], x[i]);
                int p = ds.IndexOf(u[i]);
                p = (p + 3) % 4;
                u[i] = ds[p];
            }
        }

        if (ans == long.MaxValue) cout.WriteLine("SAFE");
        else {
            cout.WriteLine(ans);
        }
    }

}

// PREWRITEN CODE BEGINS FROM HERE

static public class StringExtensions {
    static public string JoinToString<T>(this IEnumerable<T> source, string separator = " ") {
        return string.Join(separator, source);
    }
}

internal partial class Solver : Scanner {
    public static void Main() {
#if LOCAL
        byte[] inputBuffer = new byte[1000000];
        var inputStream = Console.OpenStandardInput(inputBuffer.Length);
        using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) {
            Console.SetIn(reader);
            new Solver(Console.In, Console.Out).Run();
        }
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver(Console.In, Console.Out).Run();
        Console.Out.Flush();
#endif
    }

#pragma warning disable IDE0052
    private readonly TextReader cin;
    private readonly TextWriter cout;
    private readonly TextWriter cerr;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        cin = reader;
        cout = writer;
        cerr = Console.Error;
    }

    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer) {
    }

#pragma warning disable IDE1006
#pragma warning disable IDE0051
    private int ni() { return NextInt(); }
    private int[] ni(int n) { return NextIntArray(n); }
    private long nl() { return NextLong(); }
    private long[] nl(int n) { return NextLongArray(n); }
    private double nd() { return NextDouble(); }
    private double[] nd(int n) { return NextDoubleArray(n); }
    private string ns() { return Next(); }
    private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}

#if DEBUG
internal static class LinqPadExtension {
    public static string TextDump<T>(this T obj) {
        if (obj is IEnumerable) return (obj as IEnumerable).Cast<object>().JoinToString().Dump();
        else return obj.ToString().Dump();
    }
    public static T Dump<T>(this T obj) {
        return LINQPad.Extensions.Dump(obj);
    }
}
#endif

public class Scanner {
    private readonly TextReader Reader;
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    private readonly char[] buffer = new char[2 * 1024];
    private int cursor = 0, length = 0;
    private string Token;
    private readonly StringBuilder sb = new StringBuilder(1024);

    public Scanner()
        : this(Console.In) {
    }

    public Scanner(TextReader reader) {
        Reader = reader;
    }

    public int NextInt() { return checked((int)NextLong()); }
    public long NextLong() {
        var s = Next();
        long r = 0;
        int i = 0;
        bool negative = false;
        if (s[i] == '-') {
            negative = true;
            i++;
        }
        for (; i < s.Length; i++) {
            r = r * 10 + (s[i] - '0');
#if DEBUG
            if (!char.IsDigit(s[i])) throw new FormatException();
#endif
        }
        return negative ? -r : r;
    }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size) {
        string[] array = new string[size];
        for (int i = 0; i < size; i++) {
            array[i] = Next();
        }

        return array;
    }
    public int[] NextIntArray(int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextInt();
        }

        return array;
    }

    public long[] NextLongArray(int size) {
        long[] array = new long[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextLong();
        }

        return array;
    }

    public double[] NextDoubleArray(int size) {
        double[] array = new double[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextDouble();
        }

        return array;
    }

    public string Next() {
        if (Token == null) {
            if (!StockToken()) {
                throw new Exception();
            }
        }
        var token = Token;
        Token = null;
        return token;
    }

    public bool HasNext() {
        if (Token != null) {
            return true;
        }

        return StockToken();
    }

    private bool StockToken() {
        while (true) {
            sb.Clear();
            while (true) {
                if (cursor >= length) {
                    cursor = 0;
                    if ((length = Reader.Read(buffer, 0, buffer.Length)) <= 0) {
                        break;
                    }
                }
                var c = buffer[cursor++];
                if (33 <= c && c <= 126) {
                    sb.Append(c);
                } else {
                    if (sb.Length > 0) break;
                }
            }

            if (sb.Length > 0) {
                Token = sb.ToString();
                return true;
            }

            return false;
        }
    }
}