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
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
#include <bits/stdc++.h>
using namespace std;
using I = long long; 

inline I gcd(I a, I b) {
    return (b ? gcd(b, a % b): a);
}

struct Rational {
	I p, q;

    Rational() : p(0), q(1) {}
    Rational(I a, I b) : p(a), q(b) {
        assert(q != 0);
        if (q < 0) {
            p = -p;
            q = -q;
        }

        I g = gcd(a, b);
        p /= g;
        q /= g;
    }

	void print() {
		cout << "<" << p << "/" << q << ">";
	}

    bool operator==(const Rational &rhs) const {
        return p == rhs.p && q == rhs.q;
    }

    bool operator<(const Rational &rhs) const {
	    return 1LL * p * rhs.q < 1LL * rhs.p * q;
    }

    Rational operator+(const Rational &rhs) const {
        return Rational{p * rhs.q + rhs.p * q, q * rhs.q};
    }

    Rational operator-(const Rational &rhs) const {
        return Rational{p * rhs.q - rhs.p * q, q * rhs.q};
    }

    Rational operator/(const Rational &rhs) const {
        return Rational{p * rhs.q, q * rhs.p};
    }

    Rational operator*(const Rational &rhs) const {
        return Rational{p * rhs.p, q * rhs.q};
    }
};


int L, lel;
Rational v[4];
string s;
vector<pair<Rational, Rational>> pos[4];

map<pair<Rational, Rational>, Rational> dist[4];
set<pair<Rational, Rational>> waswas[4];
Rational res = {0, 1};

int32_t main() {
    ios_base::sync_with_stdio(0);
    cin >> L;
    for (int i = 0; i <= 3; i++) {
        cin >> lel;
        v[i] = {lel, 1};
    }
    for (int i = 1; i <= 3; i++) {
        cin >> s;
        s += ".#";
        s[0] = '.';
        int l = 0;
        for (int j = 0; j <= L; j++) {
            if (s[j] == '.' && s[j + 1] == '#') {
                pos[i].push_back({{l, 1}, {j + 1, 1}});
            } else if (s[j] == '#') l = j + 1;
        }
    }

    dist[3][pos[3][0]] = Rational{0, 1};

    dist[1][pos[1][0]] = Rational{0, 1};

    dist[2][pos[2][0]] = Rational{0, 1};
    priority_queue<pair<pair<Rational, Rational>, pair<int, int>>> pq;
    pq.push({{Rational{0, 1}, Rational{0, 1}}, {3, 0}});
    
    pq.push({{Rational{0, 1}, Rational{0, 1}}, {1, 0}});

    pq.push({{Rational{0, 1}, Rational{0, 1}}, {2, 0}});
    while (!pq.empty()) {
        auto elt = pq.top();
        pq.pop();
        Rational t = elt.first.first;
        Rational z = elt.first.second;

        int pas = elt.second.first;
        int idx = elt.second.second;

        if (waswas[pas].count(pos[pas][idx])) continue;
        waswas[pas].insert(pos[pas][idx]);

        Rational x_0 = pos[pas][idx].first + v[pas] * t;
        Rational x_1 = pos[pas][idx].second + v[pas] * t;

       // x_0.print(); x_1.print(); t.print(); cerr << pas << "\n";
        // Może już moge wyprzedzić wszystkich
        if (idx + 1 == pos[pas].size()) {
            Rational e_1 = pos[1].back().first;
            Rational e_2 = pos[2].back().first;
            Rational e_3 = pos[3].back().first;

            Rational t_1 = (e_1 + v[0] * t - z) / (v[0] - v[1]);
            Rational t_2 = (e_2 + v[0] * t - z) / (v[0] - v[2]);
            Rational t_3 = (e_3 + v[0] * t - z) / (v[0] - v[3]);

            Rational t_final = max({t_1, t_2, t_3});

            res = min(res, t + t_final);
            continue;
        }

        // Przejście na pas wolniejszy
        if (pas < 3) {
            int idx = -1;
            for (auto &i : pos[pas + 1]) {
                idx++;
                Rational y_2 = i.first + v[pas + 1] * t;
                //Rational y_1 = i.second + v[pas + 1] * t;

                Rational t_1 = (y_2 - z) / (v[0] - v[pas + 1]);
                Rational t_2 = (x_1 - z - Rational{1, 1}) / (v[0] - v[pas]);
                Rational t_3 = (y_2 - x_1 + Rational{1, 1}) / (v[pas] - v[pas + 1]);

                Rational t_final = max({t_1, t_3});
                if (t_2 < t_final) continue;
                if (!dist[pas + 1].count(i) || t_final + t < dist[pas + 1][i]) {
                    dist[pas + 1][i] = t + t_final;
                    pq.push({{t + t_final, z + v[0] * (t_final - t)}, {pas + 1, idx}});
                }
            }
        }

        // Przejście na pas szybszy
        if (pas > 1) {
            int idx = -1;
            for (auto &i : pos[pas - 1]) {
                idx++;
                Rational y_2 = i.first + v[pas - 1] * t;
                //Rational y_1 = i.second + v[pas + 1] * t;

                Rational t_1 = (y_2 - z) / (v[0] - v[pas]);
                Rational t_2 = (x_1 - z - Rational{1, 1}) / (v[0] - v[pas]);
                Rational t_3 = (y_2 - x_1 + Rational{1, 1}) / (v[pas - 1] - v[pas]);

                if (min({t_2, t_3}) < t_1) continue;

                if (!dist[pas - 1].count(i) || t_1 + t < dist[pas - 1][i]) {
                    dist[pas - 1][i] = t + t_1;
                    pq.push({{t + t_1, z + v[0] * (t_1 - t)}, {pas - 1, idx}});
                }
            }
        }
    }

    cout << fixed << setprecision(10) << ((long double)res.p / res.q) << "\n";
}