Arte Valiosa

#include<bits/stdc++.h>
using namespace std;

#define ii pair<int, int>
#define X first
#define Y second

int n, m, k;

vector<int> G[2000];
int cor[2000], tempo = 1;

bool check(ii c1, ii c2, int r1, int r2) {
    return (c1.X - c2.X) * (c1.X - c2.X) + (c1.Y - c2.Y) * (c1.Y - c2.Y) <= (r1 + r2) * (r1 + r2);
}

vector<int> border(ii c, int r) {
    int x = c.X, y = c.Y;
    vector<int> b;
    if(x - r <= 0) b.push_back(k);
    if(x + r >= n) b.push_back(k + 1);
    if(y + r >= m) b.push_back(k + 2);
    if(y - r <= 0) b.push_back(k + 3);
    return b;
}

void dfs(int v) {
    cor[v] = tempo;
    for(int &w : G[v])
        if(cor[w] < tempo)
            dfs(w);
}

int32_t main() {
    vector<ii> centers;
    vector<int> raios;

    scanf(" %d %d %d", &n, &m, &k);

    for(int i = 0; i < k; i++) {
        int x, y, r;
        scanf(" %d %d %d", &x, &y, &r);
        centers.push_back({x, y});
        raios.push_back(r);
    }
    for(int i = 0; i < k; i++) {
        for(int j = i + 1; j < k; j++)
            if(check(centers[i], centers[j], raios[i], raios[j])) {
                G[i].push_back(j);
                G[j].push_back(i);
            }
        vector<int> b = border(centers[i], raios[i]);
        for(int &w : b) {
            G[w].push_back(i);
            G[i].push_back(w);
        }
    }

    bool fl = true;

    tempo++;
    dfs(k);
    if(cor[k + 1] == tempo)
        fl = false;

    tempo++;
    dfs(k + 1);
    if(cor[k + 2] == tempo or cor[k] == tempo)
        fl = false;

    tempo++;
    dfs(k + 2);
    if(cor[k + 1] == tempo or cor[k + 3] == tempo)
        fl = false;

    tempo++;
    dfs(k + 3);
    if(cor[k + 2] == tempo or cor[k] == tempo)
        fl = false;

    puts(fl ? "S" : "N");

    return 0;
}