1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
#include <map>
#include <array>
#include <string>
#include <set>

using namespace std;

#ifdef USE_CERR_LOG
#define LOG if (true) cerr
const bool LogEnabled = true;
#else
#define LOG if (false) cerr
const bool LogEnabled = false;
#endif

#ifdef USE_FILE_CIN
ifstream fin("../kul.in");
#define cin fin
#endif


typedef long long ll;
typedef unsigned long long ull;
typedef vector<vector<ull>> UnsignedMatrix;
typedef vector<ull> UnsignedVector;

struct Ball {
    unsigned idx;
    unsigned radius;
    vector<unsigned> centreBits;
    ull encodedCentre;
};

const ull Modulo = 1'000'000'007;
const unsigned BallCount = 3;
unsigned n;
unsigned maxRadius;
UnsignedMatrix distMatrix;
array<Ball, BallCount> balls;


void printBalls() {
    if (LogEnabled) {
        for (const Ball& ball : balls) {
            LOG << ball.idx << ": ";
            for (auto bit : ball.centreBits) LOG << bit;
            LOG << " " << ball.encodedCentre << endl;
        }
        
        LOG << "--------------------------------" << endl;
    }    
}

void printDistMatrix(const UnsignedMatrix& matrix) {
    if (LogEnabled) {
        int idx = 0;
        
        for (const UnsignedVector& row : matrix) {
            LOG << idx << ": ";
            for (auto num : row) LOG << num << ", ";
            LOG << endl;
            idx++;
        }
        
        LOG << "--------------------------------" << endl;
    }
}

void computeDistMatrix(unsigned radius) {
    pair<vector<vector<ull>>, vector<vector<ull>>> matrices;
    
    matrices.first.push_back({0});
    matrices.first.push_back({1});
    
    for (unsigned b=2; b<=n; b++) {
        vector<vector<ull>>& prev = (b % 2 == 0) ? matrices.first : matrices.second;
        vector<vector<ull>>& curr = (b % 2 == 0) ? matrices.second : matrices.first;
        
        curr.clear();
        curr.push_back({0});
        ull prefix = (ull) 1 << (b - 1);
        
        for (unsigned r=1; r<min(b, radius+1); r++) {
            curr.push_back(prev[r]);
            
            for (size_t i=0; i<prev[r-1].size(); i++) {
                curr[r].push_back(prev[r-1][i] + prefix);
            }
        }
        
        if (prev.size() >= b) {
            curr.push_back({prev[b-1][0] + prefix});
        }
        
        LOG << b << endl;
        // printDistMatrix(curr);
    }

    distMatrix = (n % 2 == 0) ? matrices.second : matrices.first;
}

void solve() {
    set<ull> points;
    
    for (const Ball& ball : balls) {
        for (unsigned r=0; r <= ball.radius; r++) {
            for (auto num : distMatrix[r]) {
                points.insert(num ^ ball.encodedCentre);
            }
        }
    }
    
    cout << points.size();
}

void readData() {
    cin >> n;
    string strCentre;
    maxRadius = 0;
    
    for (unsigned i=0; i<BallCount; i++) {
        Ball& ball = balls[i];
        ball.idx = i;
        ball.encodedCentre = 0;
        
        cin >> ball.radius >> strCentre;
        maxRadius = max(maxRadius, ball.radius);
        
        for (unsigned j=0; j<n; j++) {
            int bit = strCentre[j] - '0';
            ball.centreBits.push_back(bit);
            ball.encodedCentre = 2 * ball.encodedCentre + bit;
        }
    }
    
    printBalls();
}


int main() {
    ios_base::sync_with_stdio(false);
    
    readData();
    computeDistMatrix(maxRadius);
    solve();
    
    return 0;
}