Laser

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

struct BIT {
    int n;
    vector<map<int, int>> B;

    BIT(int _n) {
        n = _n;
        B.resize(n + 1);
    }

    void add(int p, int x, int d) {
        while(p <= n) {
            B[p][x] += d;
            p += (p&-p);
        }
    }

    int query(int p, int x) {
        int s = 0;
        while(p > 0) {
            s += B[p][x];
            p -= (p&-p);
        }
        return s;
    }

    int rangeQuery(int l, int r, int x) {
        return query(r, x) - query(l - 1, x);
    }
};

int main(){
    int n, m, q;

    cin >> n >> m >> q;

    vector<int> row(n + 1), col(m + 1);
    BIT rowBit(n), colBit(m);

    for(int i = 1; i <= n; ++i) {
        rowBit.add(i, 0, +1);
    }
    for(int i = 1; i <= m; ++i) {
        colBit.add(i, 0, +1);
    }

    while(q--) {
        char c;
        int x, y;

        cin >> c >> x >> y;
        if(c == 'A') {
            rowBit.add(x, row[x], -1);
            colBit.add(y, col[y], -1);
            row[x]++;
            col[y]++;
            rowBit.add(x, row[x], +1);
            colBit.add(y, col[y], +1);
        } else if(c == 'R') {
            rowBit.add(x, row[x], -1);
            colBit.add(y, col[y], -1);
            row[x]--;
            col[y]--;
            rowBit.add(x, row[x], +1);
            colBit.add(y, col[y], +1);
        } else {
            int xx, yy;
            cin >> xx >> yy;

            int lRow = min(x, xx), rRow = max(x, xx);
            int lCol = min(y, yy), rCol = max(y, yy);

            int uncoveredRows = rowBit.rangeQuery(lRow, rRow, 0);
            int uncoveredCols = colBit.rangeQuery(lCol, rCol, 0);

            if(!uncoveredRows || !uncoveredCols) {
                cout << "S\n";
            } else {
                cout << "N\n";
            }
        }
    }

    return 0;
}