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
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
#include <iostream>
#include <string>

using namespace std;

//#define DEBUG
//#define PRINTARR

int n;
struct Ball {
	int r;
	string v;
	bool inline operator<(const Ball& other) const {
		return r<other.r;
	}
	bool inline operator==(const Ball& other) const {
		return r==other.r && v==other.v;
	}
};
istream& operator>>(istream& is, Ball& b) {
	return is>>b.r>>b.v;
}

Ball b1, b2, b3;

const long long BASE = 1000000007LL;
const int MAX_N = 10002;

long long inline mod(long long res) {
	return res%BASE;
}

long long inline normalize(long long n) {
	while(n>BASE)
		n = mod(n);
	while(n<0)
		n = mod(BASE+n);
	return n;
}

long long binominal[MAX_N][MAX_N];

void precalc() {
	binominal[0][0]=1;
	for(int i=1;i<=n;++i) {
		binominal[i][0] = 1;
		long long sum=2;
		for(int j=1;j<i;++j) {
			sum += binominal[i][j] = mod(binominal[i-1][j-1]+binominal[i-1][j]);
		}
		binominal[i][i] = 1;
		binominal[i][n+1] = mod(sum);
	}
#if defined(DEBUG) && defined(PRINTARR)
	for(int i=0;i<=n;++i) {
		for(int j=0;j<=n+1;++j)
			cout<<binominal[i][j]<<" ";
		cout<<endl;
	}
#endif
}

long long inline area(const Ball& b) {
	auto type = binominal[n];
	long long result = 0LL;
	for(int i=0;i<=b.r;++i)
		result += type[i];
	return mod(result);
}

int inline dist(const Ball& b1, const Ball& b2) {
	int dist=0;
	for(auto i1 = b1.v.begin(), i2=b2.v.begin(); i1!=b1.v.end(); ++i1, ++i2)
		if(*i1 != *i2)
			++dist;
	return dist;
}

long long intersect(const Ball& b1, const Ball& b2) {
	if(b2<b1)
		return intersect(b2, b1);
	//r1<=r2
	int distance = dist(b1, b2);
#if defined(DEBUG)
	cerr<<"dist("<<b1.v<<","<<b2.v<<") = "<<distance<<endl;
#endif // defined
	if(distance > b1.r+b2.r)
		return 0LL; // not touching each other
	if(distance <= b2.r-b1.r)
		return area(b1); // b1 is fully inside b2

	//rect dist+1 x (n-dist+1)
	auto coeff1 = binominal[distance];
	auto coeff2 = binominal[n-distance];
	int i_a = distance-b1.r;
	int i_b = b2.r;
	long long intersection = 0LL;
	for(int j=0;j<=(n-distance);++j) {
		for(int i=0;i<=distance;++i) {
			bool mark = i>=i_a && i<=i_b;
			if(mark)
				intersection += mod(coeff1[i]*coeff2[j]);
#if defined(DEBUG) && defined(PRINTARR)
			//cerr<<i_a<<","<<i_b<<","<<coeff1[i]*coeff2[j]<<(mark?"+":"")<<"\t";
			cerr<<mod(coeff1[i]*coeff2[j])<<(mark?"+":" ")<<" ";
#endif
		}
#if defined(DEBUG) && defined(PRINTARR)
		cerr<<endl;
#endif
		++i_a;
		--i_b;
		if(i_a>i_b)
			break;
	}
	return mod(intersection);
}

long long intersect(const Ball& b1, const Ball& b2, const Ball& b3) {
	return 0LL;
}

long long solution2(Ball& b1, Ball& b2) {
	long long area1 = area(b1);
	long long area2 = area(b2);
	long long p12 = intersect(b1, b2);
#if defined(DEBUG)
	cerr<<area1<<endl<<area2<<endl
		<<-p12<<endl;
#endif
	return normalize(area1+area2-p12);
}

long long solution3(const Ball& b1, const Ball& b2, const Ball& b3) {
	long long area1 = area(b1);
	long long area2 = area(b2);
	long long area3 = area(b3);
	long long p12 = intersect(b1, b2);
	long long p13 = intersect(b1, b3);
	long long p23 = intersect(b2, b3);
	//one of balls is inside another - return result for 2
	if(p12==area1 || p13==area1) {
#if defined(DEBUG)
	cerr<<area2<<endl<<area3<<endl
		<<-p23<<endl;
#endif
		return normalize(area2+area3-p23);
	}
	else if(p12==area2 || p23==area2) {
#if defined(DEBUG)
	cerr<<area1<<endl<<area3<<endl
		<<-p13<<endl;
#endif
		return normalize(area1+area3-p13);
	}
	else if(p13==area3 || p23==area3) {
#if defined(DEBUG)
	cerr<<area1<<endl<<area2<<endl
		<<-p12<<endl;
#endif
		return normalize(area1+area2-p12);
	}
	//no way - we must dispatch 3 balls intersection :C
	long long p123 = intersect(b1, b2, b3);
#if defined(DEBUG)
	cerr<<area1<<endl<<area2<<endl<<area3<<endl
		<<-p12<<endl<<-p13<<endl<<-p23<<endl
		<<p123<<endl;
#endif
	return normalize(area1+area2+area3-p12-p13-p23+p123);
}

int main() {
	ios_base::sync_with_stdio(0);
	cin>>n
		>>b1>>b2>>b3;

	precalc();
	if(b1==b2)
		cout<<solution2(b1, b3);
	else if(b1==b3)
		cout<<solution2(b1, b2);
	else if(b2==b3)
		cout<<solution2(b1, b2);
	else
		cout<<solution3(b1, b2, b3);
}