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
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
#include <bits/stdc++.h>

using namespace std;

typedef long long int LL;

const int N = 10007;
const int MX = 1e9 + 7;

int n;
int r[3];
vector <int> in[3];

int pref[N];
int sum[N][N];
int newton[N][N];

void add(int &a, int b){
	a += b;
	if(a >= MX)
		a -= MX;
}

void sub(int &a, int b){
	a -= b;
	if(a < 0)
		a += MX;
}

void read(int id){
	char tmp[N];
	scanf("%d %s", &r[id], tmp);
	
	in[id].resize(n);
	for(int i = 0; i < n; ++i)
		in[id][i] = tmp[i] - '0';
}

int calc1(int fa){
	int ans = 0;
	for(int i = 0; i <= r[fa]; ++i)
		add(ans, newton[n][i]);
	return ans;
}

int calc2(int fa, int fb){
	int eq = 0, df = 0;
	for(int i = 0; i < n; ++i)
		if(in[fa][i] != in[fb][i])
			++df;
		else
			++eq;
	
	pref[0] = newton[eq][0];
	for(int i = 1; i <= eq; ++i)
		pref[i] = (newton[eq][i] + pref[i - 1]) % MX;
	
	int ans = 0;
	for(int i = 0; i <= df; ++i){
		if(i > r[fa])	break;
		if(df - i > r[fb])	continue;
		
		int Left = min(eq, min(r[fa] - i, r[fb] - df + i));
		ans = (ans + 1LL * newton[df][i] * pref[Left]) % MX;
	}
	
	return ans;
}

int calc3(){
	int ans = 0;
	int allEq = 0;
	vector <int> cnt(3, 0);
	
	for(int i = 0; i < n; ++i)
		if(in[0][i] == in[1][i] && in[1][i] == in[2][i])
			++allEq;
		else if(in[0][i] == in[1][i])
			++cnt[2];
		else if(in[1][i] == in[2][i])
			++cnt[0];
		else
			++cnt[1];
	
	for(int fa = 0; fa <= cnt[0]; ++fa)
		for(int fb = 0; fb <= cnt[1]; ++fb){
			int downLimit = max(fa + fb + cnt[2] - r[2], 0);
			int upLimit = min(min(r[0] + fa - cnt[0] - fb, r[1] + fb - cnt[1] - fa), cnt[2]);
			
			if(downLimit > upLimit)
				continue;
			
			int LeftX = r[2] - fa - fb - cnt[2] + downLimit;
			int RightX = min(r[0] + fa - cnt[0] - fb - upLimit, r[1] + fb - cnt[1] - fa - upLimit);
//			printf("%d %d\n", LeftX, RightX);
			int tmpSum = RightX - LeftX + upLimit - downLimit;
			int midOption = tmpSum / 2;
			
			if(tmpSum < 0)
				midOption = -1;
			midOption += downLimit;

			int newtVal = (1LL * newton[cnt[0]][fa] * newton[cnt[1]][fb]) % MX;
			midOption = min(midOption, upLimit);

			if(downLimit <= midOption){
//				printf("%d -> %d dodaje %d -> %d o wart %d\n", downLimit, midOption, LeftX, LeftX + midOption - downLimit, newtVal);
				add(sum[downLimit][LeftX], newtVal);
				add(sum[midOption + 1][LeftX + midOption - downLimit + 1], MX - newtVal);
			}
		}

	pref[0] = newton[allEq][0];
	for(int i = 1; i <= n; ++i)
		pref[i] = (pref[i - 1] + newton[allEq][i]) % MX;

	for(int i = 0; i <= cnt[2]; ++i)
		for(int j = 0; j <= n; ++j){
			if(i && j)
				add(sum[i][j], sum[i - 1][j - 1]);

			ans = (ans + ((1LL * newton[cnt[2]][i] * sum[i][j]) % MX) * pref[j]) % MX;
		}

	for(int i = 0; i <= cnt[2]; ++i)
		for(int j = 0; j <= n; ++j)
			sum[i][j] = 0;

	for(int fa = 0; fa <= cnt[0]; ++fa)
		for(int fb = 0; fb <= cnt[1]; ++fb){
			int downLimit = max(fa + fb + cnt[2] - r[2], 0);
			int upLimit = min(min(r[0] + fa - cnt[0] - fb, r[1] + fb - cnt[1] - fa), cnt[2]);
			
			if(downLimit > upLimit)
				continue;
			
			int LeftX = r[2] - fa - fb - cnt[2] + downLimit;
			int RightX = min(r[0] + fa - cnt[0] - fb - upLimit, r[1] + fb - cnt[1] - fa - upLimit);
			
			int tmpSum = RightX - LeftX + upLimit - downLimit;
			int midOption = tmpSum / 2;
			
			if(tmpSum < 0)
				midOption = -1;
			midOption += downLimit;

			int newtVal = (1LL * newton[cnt[0]][fa] * newton[cnt[1]][fb]) % MX;
			midOption = max(midOption, downLimit - 1);

			if(midOption < upLimit){
//				printf("%d -> %d dodaje %d -> %d o wart %d\n", upLimit, midOption + 1, RightX, RightX + upLimit - midOption - 1, newtVal);
				add(sum[upLimit][RightX], newtVal);
				if(midOption >= 0)
					add(sum[midOption][RightX + upLimit - midOption], MX - newtVal);
			}
		}

	for(int i = cnt[2]; i >= 0; --i)
		for(int j = 0; j <= n; ++j){
			if(i < cnt[2] && j)
				add(sum[i][j], sum[i + 1][j - 1]);
			
//			if(sum[i][j] != 0)
//				printf("%d %d %d\n", i, j, sum[i][j]);
			ans = (ans + ((1LL * newton[cnt[2]][i] * sum[i][j]) % MX) * pref[j]) % MX;
		}

	for(int i = 0; i <= cnt[2]; ++i)
		for(int j = 0; j <= n; ++j)
			sum[i][j] = 0;
	return ans;
}

int main(){
	scanf("%d", &n);
	for(int i = 0; i < 3; ++i)
		read(i);
	
	for(int i = 0; i <= n; ++i){
		newton[i][0] = newton[i][i] = 1;
		for(int j = 1; j < i; ++j){
			add(newton[i][j], newton[i - 1][j - 1]);
			add(newton[i][j], newton[i - 1][j]);
		}
	}
	
	LL ans = 0;
	for(int i = 0; i < 3; ++i)
		ans += calc1(i);
	
	ans -= calc2(0, 1);
	ans -= calc2(0, 2);
	ans -= calc2(1, 2);
	ans += calc3();
	
	ans %= MX;
	ans += MX;
	ans %= MX;
	
//	printf("%d %d %d %d %d %d %d\n", calc1(0), calc1(1), calc1(2), calc2(0, 1), calc2(0, 2), calc2(1, 2), calc3());
	printf("%lld\n", ans);
	return 0;
}