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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using static Assistant.Input;
using static Assistant.Debug;
using System.Linq;
using Assistant;

namespace MSOL2020F
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = RInt;

            List<Pos> U = new List<Pos>();
            List<Pos> D = new List<Pos>();
            List<Pos> L = new List<Pos>();
            List<Pos> R = new List<Pos>();
            List<Pos>[] U2 = new List<Pos>[200010].Select(x => new List<Pos>()).ToArray();
            List<Pos>[] D2 = new List<Pos>[200010].Select(x => new List<Pos>()).ToArray();
            List<Pos>[] L2 = new List<Pos>[200010].Select(x => new List<Pos>()).ToArray();
            List<Pos>[] R2 = new List<Pos>[200010].Select(x => new List<Pos>()).ToArray();
            List<Pos>[] Lm = new List<Pos>[400010].Select(x => new List<Pos>()).ToArray();
            List<Pos>[] Lp = new List<Pos>[400010].Select(x => new List<Pos>()).ToArray();
            List<Pos>[] Rm = new List<Pos>[400010].Select(x => new List<Pos>()).ToArray();
            List<Pos>[] Rp = new List<Pos>[400010].Select(x => new List<Pos>()).ToArray();
            for (int i = 0; i < N; i++)
            {
                var x = RInt;
                var y = RInt;
                var s = RString;
                var p = new Pos(x, y);
                if (s == "U")
                {
                    U.Add(p);
                    U2[p.x].Add(p);
                }
                else if (s == "D")
                {
                    D.Add(p);
                    D2[p.x].Add(p);
                }
                else if (s == "L")
                {
                    L.Add(p);
                    Lm[p.m].Add(p);
                    Lp[p.p].Add(p);
                    L2[p.y].Add(p);
                }
                else if (s == "R")
                {
                    R.Add(p);
                    Rm[p.m].Add(p);
                    Rp[p.p].Add(p);
                    R2[p.y].Add(p);
                }
            }

            int ans = int.MaxValue;
            // ①
            foreach (var p in U)
            {
                var candm = Lm[p.m];
                foreach (var cp in candm)
                {
                    if (cp.x > p.x && cp.y > p.y)
                    {
                        ans = Math.Min(ans, (cp.y - p.y) * 10);
                    }
                }
                var candp = Rp[p.p];
                foreach (var cp in candp)
                {
                    if (cp.x < p.x && cp.y > p.y)
                    {
                        ans = Math.Min(ans, (cp.y - p.y) * 10);
                    }
                }
            }
            // ②
            foreach (var p in D)
            {
                var candp = Lp[p.p];
                foreach (var cp in candp)
                {
                    if (cp.x > p.x && cp.y < p.y)
                    {
                        ans = Math.Min(ans, (p.y - cp.y) * 10);
                    }
                }
                var candm = Rm[p.m];
                foreach (var cp in candm)
                {
                    if (cp.x < p.x && cp.y < p.y)
                    {
                        ans = Math.Min(ans, (p.y - cp.y) * 10);
                    }
                }
            }

            // ③
            int[][] Darr = new int[200010][];
            int[][] Larr = new int[200010][];
            for (int i = 0; i < 200010; i++)
            {
                Darr[i] = D2[i].Select(a => a.y).OrderBy(a => a).ToArray();
                Larr[i] = L2[i].Select(a => a.x).OrderBy(a => a).ToArray();
            }
            foreach (var u in U)
            {
                if (Darr[u.x].Length == 0) continue;
                int ind = LowerBound(Darr[u.x], u.y);
                if (ind < Darr[u.x].Length) ans = Math.Min(ans, (Darr[u.x][ind] - u.y) * 10 / 2);
            }
            foreach (var r in R)
            {
                if (Larr[r.y].Length == 0) continue;
                int ind = LowerBound(Larr[r.y], r.x);
                if (ind < Larr[r.y].Length) ans = Math.Min(ans, (Larr[r.y][ind] - r.x) * 10 / 2);
            }

            if (ans != int.MaxValue) Console.WriteLine(ans);
            else Console.WriteLine("SAFE");
        }

        public static int LowerBound<T>(T[] a, T v)
        {
            return LowerBound(a, v, Comparer<T>.Default);
        }
        public static int LowerBound<T>(T[] a, T v, Comparer<T> cmp)
        {
            var l = 0;
            var r = a.Length - 1;
            while (l <= r)
            {
                var mid = l + (r - l) / 2;
                var res = cmp.Compare(a[mid], v);
                if (res == -1) l = mid + 1;
                else r = mid - 1;
            }
            return l;
        }

        struct Pos
        {
            public int x;
            public int y;
            public int m => (x - y) + 200000;
            public int p => (x + y);
            public Pos(int x, int y)
            {
                this.x = x;
                this.y = y;
            }
        }

    }


}

namespace Assistant
{
    static class Input
    {
        static List<string> line = new List<string>();
        static int index = 0;
        static String RNext()
        {
            if (line.Count <= index) line.AddRange(Console.ReadLine().Split());
            return line[index++];
        }
        public static int RInt => int.Parse(RNext());
        public static long RLong => long.Parse(RNext());
        public static int[] RInts => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] RLongs => Console.ReadLine().Split().Select(long.Parse).ToArray();
        public static string RString => RNext();
        //以下未テスト
        public static int[] RIntsC(int c) => Enumerable.Repeat(0, c).Select(x => int.Parse(RNext())).ToArray();
        public static long[] RLongsC(int c) => Enumerable.Repeat(0, c).Select(x => long.Parse(RNext())).ToArray();
        public static char[][] RMap(int h) => Enumerable.Repeat(0, h).Select(x => Console.ReadLine().ToCharArray()).ToArray();
    }

    public struct Mlong
    {
        long _v;
        const long mod = 1000000007;
        public Mlong(long n = 0) : this() { _v = n >= mod ? n % mod : n; }

        public static implicit operator Mlong(long _x) => new Mlong(_x);
        public static implicit operator long(Mlong _x) => _x._v;
        public static Mlong operator +(Mlong m1, Mlong m2) { long m = m1._v + m2._v; return m >= mod ? m - mod : m; }
        public static Mlong operator -(Mlong m1, Mlong m2) { long m = m1._v - m2._v; return m >= 0 ? m : m + mod; }
        public static Mlong operator *(Mlong m1, Mlong m2) => m1._v * m2._v % mod;
        public static Mlong operator /(Mlong m1, Mlong m2) => m1._v * ModPow(m2._v, mod - 2) % mod;

        public static long ModPow(long a, long n)
        {
            if (n == 0) return 1;
            else if (n % 2 == 1) return a * ModPow(a, n - 1) % mod;
            else return ModPow(a * a % mod, n / 2);
        }

        static Mlong[] fac, finv, inv;
        public static void nCkInit(int max)
        {
            fac = new Mlong[max]; finv = new Mlong[max]; inv = new Mlong[max];
            fac[0] = fac[1] = 1;
            finv[0] = finv[1] = 1;
            inv[1] = 1;
            for (int i = 2; i < max; i++)
            {
                fac[i] = fac[i - 1] * i;
                inv[i] = mod - inv[mod % i] * (mod / i);
                finv[i] = finv[i - 1] * inv[i];
            }
        }

        public static Mlong nCk(int n, int k)
        {
            if (n < k) return 0;
            if (n < 0 || k < 0) return 0;
            return fac[n] * finv[k] * finv[n - k];
        }
    }

    static class Debug
    {
        static public void Draw2D<T>(T[,] map, int mode = 1)
        {
#if DEBUG
            int W = map.GetLength(0);
            int H = map.GetLength(1);

            string[,] map2 = new string[W + 1, H + 1];
            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (i == 0 && j == 0) map2[i, j] = 0.ToString();
                    else if (i == 0) map2[i, j] = (j - 1).ToString();
                    else if (j == 0) map2[i, j] = (i - 1).ToString();
                    else map2[i, j] = map[i - 1, j - 1].ToString();
                }
            }

            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (mode == 0) Console.Write(map2[i, j].Last());
                    if (mode == 1) Console.Write(map2[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
#endif
        }

        public static void Draw1D<T>(T[] array, int mode = 0)
        {
#if DEBUG
            Console.WriteLine(string.Join(" ", array));
#endif
        }
    }
}