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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb(x) push_back(x)
#define mp(a, b) make_pair(a, b)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define lscan(x) scanf("%I64d", &x)
#define lprint(x) printf("%I64d", x)
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep2(i, n) for (int i = n - 1; i >= 0; i--)
const int mod = 1000000007;
ll gcd(ll a, ll b)
{
	ll c = a % b;
	while (c != 0)
	{
		a = b;
		b = c;
		c = a % b;
	}
	return b;
}
long long extGCD(long long a, long long b, long long &x, long long &y)
{
	if (b == 0)
	{
		x = 1;
		y = 0;
		return a;
	}
	long long d = extGCD(b, a % b, y, x);
	y -= a / b * x;
	return d;
}

struct UnionFind
{
	vector<ll> data;

	UnionFind(int sz)
	{
		data.assign(sz, -1);
	}

	bool unite(int x, int y)
	{
		x = find(x), y = find(y);
		if (x == y)
			return (false);
		if (data[x] > data[y])
			swap(x, y);
		data[x] += data[y];
		data[y] = x;
		return (true);
	}

	int find(int k)
	{
		if (data[k] < 0)
			return (k);
		return (data[k] = find(data[k]));
	}

	ll size(int k)
	{
		return (-data[find(k)]);
	}
};

ll M = 1000000007;

vector<ll> fac(2000011);  //n!(mod M)
vector<ll> ifac(2000011); //k!^{M-2} (mod M)

ll mpow(ll x, ll n)
{
	ll ans = 1;
	while (n != 0)
	{
		if (n & 1)
			ans = ans * x % M;
		x = x * x % M;
		n = n >> 1;
	}
	return ans;
}
ll mpow2(ll x, ll n, ll mod)
{
	ll ans = 1;
	while (n != 0)
	{
		if (n & 1)
			ans = ans * x % mod;
		x = x * x % mod;
		n = n >> 1;
	}
	return ans;
}
void setcomb()
{
	fac[0] = 1;
	ifac[0] = 1;
	for (ll i = 0; i < 2000010; i++)
	{
		fac[i + 1] = fac[i] * (i + 1) % M; // n!(mod M)
	}
	ifac[2000010] = mpow(fac[2000010], M - 2);
	for (ll i = 2000010; i > 0; i--)
	{
		ifac[i - 1] = ifac[i] * i % M;
	}
}
ll comb(ll a, ll b)
{
	if (a == 0 && b == 0)
		return 1;
	if (a < b || a < 0)
		return 0;
	ll tmp = ifac[a - b] * ifac[b] % M;
	return tmp * fac[a] % M;
}
ll perm(ll a, ll b)
{
	if (a == 0 && b == 0)
		return 1;
	if (a < b || a < 0)
		return 0;
	return fac[a] * ifac[a - b] % M;
}
long long modinv(long long a)
{
	long long b = M, u = 1, v = 0;
	while (b)
	{
		long long t = a / b;
		a -= t * b;
		swap(a, b);
		u -= t * v;
		swap(u, v);
	}
	u %= M;
	if (u < 0)
		u += M;
	return u;
}
ll modinv2(ll a, ll mod)
{
	ll b = mod, u = 1, v = 0;
	while (b)
	{
		ll t = a / b;
		a -= t * b;
		swap(a, b);
		u -= t * v;
		swap(u, v);
	}
	u %= mod;
	if (u < 0)
		u += mod;
	return u;
}

template <int mod>
struct ModInt
{
	int x;

	ModInt() : x(0) {}

	ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

	ModInt &operator+=(const ModInt &p)
	{
		if ((x += p.x) >= mod)
			x -= mod;
		return *this;
	}

	ModInt &operator-=(const ModInt &p)
	{
		if ((x += mod - p.x) >= mod)
			x -= mod;
		return *this;
	}

	ModInt &operator*=(const ModInt &p)
	{
		x = (int)(1LL * x * p.x % mod);
		return *this;
	}

	ModInt &operator/=(const ModInt &p)
	{
		*this *= p.inverse();
		return *this;
	}

	ModInt operator-() const { return ModInt(-x); }

	ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

	ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

	ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

	ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

	bool operator==(const ModInt &p) const { return x == p.x; }

	bool operator!=(const ModInt &p) const { return x != p.x; }

	ModInt inverse() const
	{
		int a = x, b = mod, u = 1, v = 0, t;
		while (b > 0)
		{
			t = a / b;
			swap(a -= t * b, b);
			swap(u -= t * v, v);
		}
		return ModInt(u);
	}

	ModInt pow(int64_t n) const
	{
		ModInt ret(1), mul(x);
		while (n > 0)
		{
			if (n & 1)
				ret *= mul;
			mul *= mul;
			n >>= 1;
		}
		return ret;
	}

	friend ostream &operator<<(ostream &os, const ModInt &p)
	{
		return os << p.x;
	}

	friend istream &operator>>(istream &is, ModInt &a)
	{
		int64_t t;
		is >> t;
		a = ModInt<mod>(t);
		return (is);
	}

	static int get_mod() { return mod; }
};

using mint = ModInt<mod>;

vector<vector<ll>> mul(vector<vector<ll>> a, vector<vector<ll>> b, int n)
{
	int i, j, k, t;
	vector<vector<ll>> c(n);
	for (i = 0; i < n; i++)
	{
		for (j = 0; j < n; j++)
		{
			t = 0;
			for (k = 0; k < n; k++)
				t = (t + a[i][k] * b[k][j] % M) % M;
			c[i].push_back(t);
		}
	}
	return c;
}

template <typename Monoid>
struct SegmentTree
{
	using F = function<Monoid(Monoid, Monoid)>;

	int sz;
	vector<Monoid> seg;

	const F f;
	const Monoid M1;

	SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1)
	{
		sz = 1;
		while (sz < n)
			sz <<= 1;
		seg.assign(2 * sz, M1);
	}

	void set(int k, const Monoid &x)
	{
		seg[k + sz] = x;
	}

	void build()
	{
		for (int k = sz - 1; k > 0; k--)
		{
			seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
		}
	}

	void update(int k, const Monoid &x)
	{
		k += sz;
		seg[k] = x;
		while (k >>= 1)
		{
			seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
		}
	}

	Monoid query(int a, int b)
	{
		Monoid L = M1, R = M1;
		for (a += sz, b += sz; a < b; a >>= 1, b >>= 1)
		{
			if (a & 1)
				L = f(L, seg[a++]);
			if (b & 1)
				R = f(seg[--b], R);
		}
		return f(L, R);
	}

	Monoid operator[](const int &k) const
	{
		return seg[k + sz];
	}

	template <typename C>
	int find_subtree(int a, const C &check, Monoid &M, bool type)
	{
		while (a < sz)
		{
			Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
			if (check(nxt))
				a = 2 * a + type;
			else
				M = nxt, a = 2 * a + 1 - type;
		}
		return a - sz;
	}

	template <typename C>
	int find_first(int a, const C &check)
	{
		Monoid L = M1;
		if (a <= 0)
		{
			if (check(f(L, seg[1])))
				return find_subtree(1, check, L, false);
			return -1;
		}
		int b = sz;
		for (a += sz, b += sz; a < b; a >>= 1, b >>= 1)
		{
			if (a & 1)
			{
				Monoid nxt = f(L, seg[a]);
				if (check(nxt))
					return find_subtree(a, check, L, false);
				L = nxt;
				++a;
			}
		}
		return -1;
	}

	template <typename C>
	int find_last(int b, const C &check)
	{
		Monoid R = M1;
		if (b >= sz)
		{
			if (check(f(seg[1], R)))
				return find_subtree(1, check, R, true);
			return -1;
		}
		int a = sz;
		for (b += sz; a < b; a >>= 1, b >>= 1)
		{
			if (b & 1)
			{
				Monoid nxt = f(seg[--b], R);
				if (check(nxt))
					return find_subtree(b, check, R, true);
				R = nxt;
			}
		}
		return -1;
	}
};

template <unsigned mod>
struct RollingHash
{
	vector<unsigned> hashed, power;

	inline unsigned mul(unsigned a, unsigned b) const
	{
		unsigned long long x = (unsigned long long)a * b;
		unsigned xh = (unsigned)(x >> 32), xl = (unsigned)x, d, m;
		asm("divl %4; \n\t"
			: "=a"(d), "=d"(m)
			: "d"(xh), "a"(xl), "r"(mod));
		return m;
	}

	RollingHash(const string &s, unsigned base = 10007)
	{
		int sz = (int)s.size();
		hashed.assign(sz + 1, 0);
		power.assign(sz + 1, 0);
		power[0] = 1;
		for (int i = 0; i < sz; i++)
		{
			power[i + 1] = mul(power[i], base);
			hashed[i + 1] = mul(hashed[i], base) + s[i];
			if (hashed[i + 1] >= mod)
				hashed[i + 1] -= mod;
		}
	}

	unsigned get(int l, int r) const
	{
		unsigned ret = hashed[r] + mod - mul(hashed[l], power[r - l]);
		if (ret >= mod)
			ret -= mod;
		return ret;
	}

	unsigned connect(unsigned h1, int h2, int h2len) const
	{
		unsigned ret = mul(h1, power[h2len]) + h2;
		if (ret >= mod)
			ret -= mod;
		return ret;
	}

	int LCP(const RollingHash<mod> &b, int l1, int r1, int l2, int r2)
	{
		int len = min(r1 - l1, r2 - l2);
		int low = -1, high = len + 1;
		while (high - low > 1)
		{
			int mid = (low + high) / 2;
			if (get(l1, l1 + mid) == b.get(l2, l2 + mid))
				low = mid;
			else
				high = mid;
		}
		return (low);
	}
};

using RH = RollingHash<1000000007>;

template <typename T>
struct edge
{
	int src, to;
	T cost;

	edge(int to, T cost) : src(-1), to(to), cost(cost) {}

	edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

	edge &operator=(const int &x)
	{
		to = x;
		return *this;
	}

	operator int() const { return to; }
};

template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
template <typename T>
using Matrix = vector<vector<T>>;

template <typename G>
struct DoublingLowestCommonAncestor
{
	const int LOG;
	vector<int> dep;
	const G &g;
	vector<vector<int>> table;

	DoublingLowestCommonAncestor(const G &g) : g(g), dep(g.size()), LOG(32 - __builtin_clz(g.size()))
	{
		table.assign(LOG, vector<int>(g.size(), -1));
	}

	void dfs(int idx, int par, int d)
	{
		table[0][idx] = par;
		dep[idx] = d;
		for (auto &to : g[idx])
		{
			if (to != par)
				dfs(to, idx, d + 1);
		}
	}

	void build()
	{
		dfs(0, -1, 0);
		for (int k = 0; k + 1 < LOG; k++)
		{
			for (int i = 0; i < table[k].size(); i++)
			{
				if (table[k][i] == -1)
					table[k + 1][i] = -1;
				else
					table[k + 1][i] = table[k][table[k][i]];
			}
		}
	}

	int query(int u, int v)
	{
		if (dep[u] > dep[v])
			swap(u, v);
		for (int i = LOG - 1; i >= 0; i--)
		{
			if (((dep[v] - dep[u]) >> i) & 1)
				v = table[i][v];
		}
		if (u == v)
			return u;
		for (int i = LOG - 1; i >= 0; i--)
		{
			if (table[i][u] != table[i][v])
			{
				u = table[i][u];
				v = table[i][v];
			}
		}
		return table[0][u];
	}
};

int main()
{
	ll n, x[222222], y[222222], i, j, k, ans = 1e9;
	char u[222222];
	cin>>n;
	for (i = 0; i < n;i++){
		cin >> x[i] >> y[i] >> u[i];
		x[i]++;
		y[i]++;
	}
	map<ll, ll> mpc[4][2][2], mp[4];
	for (i = 0; i < n;i++){
		if(u[i]=='R'){
			if(mp[0][y[i]] == 0)
				mp[0][y[i]] = x[i];
			else
				mp[0][y[i]] = min(mp[0][y[i]], x[i]);
			for (j = 0; j < 2;j++){
				for (k = 0; k < 2;k++){
					ll p;
					if(j==0)
						p = x[i] - y[i];
					else
						p = x[i] + y[i];
					if(mpc[0][j][k][p]==0)
						mpc[0][j][k][p] = x[i];
					else{
						if (k == 0)
							mpc[0][j][k][p] = min(mpc[0][j][k][p], x[i]);
						else
							mpc[0][j][k][p] = max(mpc[0][j][k][p], x[i]);
					}
				}
			}
			if (mp[1][y[i]] > 0)
				if (x[i] < mp[1][y[i]])
					ans = min(ans, (mp[1][y[i]] - x[i]) * 5);
			if(mpc[2][1][1][x[i]+y[i]] > 0)
				if (x[i] < mpc[2][1][1][x[i] + y[i]])
					ans = min(ans, (mpc[2][1][1][x[i] + y[i]] - x[i]) * 10);
			if (mpc[3][0][1][x[i] - y[i]] > 0)
				if (x[i] < mpc[3][0][1][x[i] - y[i]])
					ans = min(ans, (mpc[3][0][1][x[i] - y[i]] - x[i]) * 10);
		}
		if(u[i]=='L'){
			if (mp[1][y[i]] == 0)
				mp[1][y[i]] = x[i];
			else
				mp[1][y[i]] = max(mp[1][y[i]], x[i]);
			for (j = 0; j < 2; j++)
			{
				for (k = 0; k < 2; k++)
				{
					ll p;
					if (j == 0)
						p = x[i] - y[i];
					else
						p = x[i] + y[i];
					if (mpc[1][j][k][p] == 0)
						mpc[1][j][k][p] = x[i];
					else
					{
						if (k == 0)
							mpc[1][j][k][p] = min(mpc[1][j][k][p], x[i]);
						else
							mpc[1][j][k][p] = max(mpc[1][j][k][p], x[i]);
					}
				}
			}
			if (mp[0][y[i]] > 0)
				if (x[i] > mp[0][y[i]])
					ans = min(ans, (x[i] - mp[0][y[i]]) * 5);
			if (mpc[2][0][1][x[i] - y[i]] > 0)
				if (x[i] > mpc[2][0][1][x[i] - y[i]])
					ans = min(ans, (x[i] - mpc[2][0][1][x[i] - y[i]]) * 10);
			if (mpc[3][1][1][x[i] + y[i]] > 0)
				if (x[i] > mpc[3][1][1][x[i] + y[i]])
					ans = min(ans, (x[i] - mpc[3][1][1][x[i] + y[i]]) * 10);
		}
		if(u[i]=='U'){
			if (mp[2][x[i]] == 0)
				mp[2][x[i]] = y[i];
			else
				mp[2][x[i]] = min(mp[2][x[i]], y[i]);
			for (j = 0; j < 2; j++)
			{
				for (k = 0; k < 2; k++)
				{
					ll p;
					if (j == 0)
						p = x[i] - y[i];
					else
						p = x[i] + y[i];
					if (mpc[2][j][k][p] == 0)
						mpc[2][j][k][p] = x[i];
					else
					{
						if (k == 0)
							mpc[2][j][k][p] = min(mpc[2][j][k][p], x[i]);
						else
							mpc[2][j][k][p] = max(mpc[2][j][k][p], x[i]);
					}
				}
			}
			if (mp[3][x[i]] > 0)
				if (y[i] < mp[3][x[i]])
					ans = min(ans, (mp[3][x[i]] - y[i]) * 5);
			if (mpc[0][1][1][x[i] + y[i]] > 0)
				if (x[i] > mpc[0][1][1][x[i] + y[i]])
					ans = min(ans, (x[i] - mpc[0][1][1][x[i] + y[i]]) * 10);
			if (mpc[1][0][1][x[i] - y[i]] > 0)
				if (x[i] < mpc[1][0][1][x[i] - y[i]])
					ans = min(ans, (mpc[1][0][1][x[i] - y[i]] - x[i]) * 10);
		}
		if(u[i]=='D'){
			if (mp[3][x[i]] == 0)
				mp[3][x[i]] = y[i];
			else
				mp[3][x[i]] = max(mp[3][x[i]], y[i]);
			for (j = 0; j < 2; j++)
			{
				for (k = 0; k < 2; k++)
				{
					ll p;
					if (j == 0)
						p = x[i] - y[i];
					else
						p = x[i] + y[i];
					if (mpc[3][j][k][p] == 0)
						mpc[3][j][k][p] = x[i];
					else
					{
						if (k == 0)
							mpc[3][j][k][p] = min(mpc[3][j][k][p], x[i]);
						else
							mpc[3][j][k][p] = max(mpc[3][j][k][p], x[i]);
					}
				}
			}
			if (mp[2][x[i]] > 0)
				if (y[i] > mp[2][x[i]])
					ans = min(ans, (y[i] - mp[2][x[i]]) * 5);
			if (mpc[0][0][1][x[i] - y[i]] > 0)
				if (x[i] > mpc[0][0][1][x[i] - y[i]])
					ans = min(ans, (x[i] - mpc[0][0][1][x[i] - y[i]]) * 10);
			if (mpc[1][1][1][x[i] + y[i]] > 0)
				if (x[i] < mpc[1][1][1][x[i] + y[i]])
					ans = min(ans, (mpc[1][1][1][x[i] + y[i]] - x[i]) * 10);
		}
	}
	if(ans>1e8)
		cout << "SAFE" << endl;
	else
		cout << ans << endl;
}