#define READ_NUM_TEST_CASES  false
#define USE_FAST_IO          false
#define USE_FAST_ENDL        true

////////////////////////////////////////////////////////////////////////////////
// AMALGAMATE: "include/template.hpp" BEGINS HERE
//
	
	
	#include <bits/stdc++.h>
	using namespace std;
	
	
	////////////////////////////////////////////////////////////////////////////////
	// AMALGAMATE: "include/abbrevs.hpp" BEGINS HERE
	//
		
		#define UI unsigned int
		
		#define LL long long
		#define ULL unsigned long long
		
		#define PII pair<int,int>
		
		
		#define RI ri()
		#define RUI rui()
		
		#define RLL rll()
		#define RULL rull()
		
		#define RSTR rstr()
		
		
		
		#define FO(i,a,b) for(int i=(a); i<int(b); ++i)
		#define OF(i,a,b) for(int i=(b)-1; i>=int(a); --i)
		
		#define FOR(i,n) FO(i,0,n)
		#define ROF(i,n) OF(i,0,n)
		
		
		#define MIN(a,b) ((a)<(b) ? (a) : (b))
		#define MAX(a,b) ((b)<(a) ? (a) : (b))
		
		#define REMIN(a,b) ((a) = min(a,b))
		#define REMAX(a,b) ((a) = max(a,b))
		
		#define ALL(c) (c).begin(),(c).end()
		
		#define SQR(x) ((x)*(x))
		
		
		
		bool is_pow(int x) {
			return (x&(x-1)) == 0;
		}
		
	
	//
	// AMALGAMATE: "include/abbrevs.hpp" ENDS HERE
	////////////////////////////////////////////////////////////////////////////////
	
	
	#if USE_FAST_IO
		
		////////////////////////////////////////////////////////////////////////////////
		// AMALGAMATE: "include/fast-io.hpp" BEGINS HERE
		//
			
			
			//#define FREAD  fread
			//#define FWRITE fwrite
			
			#define FREAD  fread_unlocked
			#define FWRITE fwrite_unlocked
			
			
			
			
			
			
			struct Buffer {
				FILE* const stream;
				const int buffer_size;
			
				uint8_t* const buff;
				int pos = 0;
			
				Buffer(FILE* a_stream, int a_buffer_size) :
						stream( a_stream ),
						buffer_size( a_buffer_size ),
						buff( new uint8_t[ buffer_size ] ) {
					setvbuf(stream, NULL, _IONBF, 0);
				}
			
				~Buffer() {
					delete[] buff;
				}
			};
			
			
			
			
			
			
			
			
			
			
			class In_Buffer : private Buffer {
			public:
				In_Buffer(FILE* a_stream, int a_buffer_size) : Buffer(a_stream, a_buffer_size) {
					FREAD(buff, 1, buffer_size, stream);
				}
			
			public:
				void prepare(int num_chars) {
					auto remaining = buffer_size - pos;
					if(remaining >= num_chars) return;
			
					assert(remaining >= 0); // prevent compiler warning
					memcpy(buff, buff+pos, remaining);
			
					int read = FREAD(buff+remaining, 1, pos, stream);
					int block_end = remaining + read;
					memset(buff + block_end, 0, buffer_size - block_end);
					pos = 0;
				}
			
			public:
				char get_unchecked() {
					return buff[ pos++ ];
				}
			};
			
			
			template<class INT>
			INT read_unsigned(In_Buffer& buff) {
				buff.prepare(25);
			
				char c = buff.get_unchecked();
				while(c < '-') c = buff.get_unchecked();
			
				INT r = 0;
			
				for(;;) {
					if(c < '0') return r;
					c -= '0';
					r = r*10 + c;
					c = buff.get_unchecked();
				}
			}
			
			
			template<class INT>
			INT read_signed(In_Buffer& buff) {
				buff.prepare(25);
			
				char c = buff.get_unchecked();
				while(c < '-') c = buff.get_unchecked();
			
				bool minus = false;
				if(c=='-') {
					c = buff.get_unchecked();
					minus = true;
				}
			
				INT r = 0;
			
				for(;;)
				{
					if(c < '0') return minus ? -r : r;
					r = r*10 + (c-'0');
					c = buff.get_unchecked();
				}
			}
			
			
			
			
			In_Buffer& operator>>( In_Buffer& buff, char& c) {
				buff.prepare(1);
				c = buff.get_unchecked();
				return buff;
			}
			
			
			
			In_Buffer& operator>>( In_Buffer& buff, UI& r) { r = read_unsigned<UI>(buff); return buff; }
			In_Buffer& operator>>( In_Buffer& buff, ULL& r) { r = read_unsigned<ULL>(buff); return buff; }
			
			In_Buffer& operator>>( In_Buffer& buff, int& r) { r = read_signed<int>(buff); return buff; }
			In_Buffer& operator>>( In_Buffer& buff, LL& r) { r = read_signed<LL>(buff); return buff; }
			
			In_Buffer& operator>>( In_Buffer& buff, string& r) {
				r.clear();
			
				char c = buff.get_unchecked();
				while(c <= ' ') c = buff.get_unchecked();
			
				do {
					r.push_back( c );
					c = buff.get_unchecked();
				} while(c > ' ');
			
				return buff;
			}
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			class Out_Buffer : private Buffer {
			public:
				Out_Buffer(FILE* a_stream, int a_buffer_size) : Buffer(a_stream, a_buffer_size) {}
			
				~Out_Buffer() {
					flush();
				}
			
			public:
				void prepare(int num_chars) {
					if(buffer_size - pos >= num_chars) return;
					flush();
				}
			
				void flush() {
					FWRITE(buff, 1, pos, stream);
					pos = 0;
				}
			
			public:
				void put_unchecked(const char& c) {
					buff[ pos++ ] = c;
				}
			
				void put_unchecked(const char* str, int len) {
					memcpy(buff+pos, str, len);
					pos += len;
				}
			};
			
			
			
			
			
			
			template<class INT>
			void write_signed(Out_Buffer& buff, const INT& i) {
				buff.prepare(25);
			
				if(i == 0) {
					buff.put_unchecked('0');
					return;
				}
			
				auto ci = i;
			
				if(ci < 0) {
					buff.put_unchecked('-');
					ci = -ci;
				}
			
				const int sz = 25;
				char temp[sz];
				int pos = sz;
			
				while(ci) {
					temp[ --pos ] = '0' + ci%10;
					ci/=10;
				}
			
				buff.put_unchecked(temp+pos, sz-pos);
			}
			
			
			
			template<class INT>
			void write_unsigned(Out_Buffer& buff, const INT& i) {
				buff.prepare(25);
			
				if(i==0) {
					buff.put_unchecked('0');
					return;
				}
			
				const int sz = 25;
				char temp[sz];
				int pos = sz;
			
				auto ci = i;
			
				while(ci) {
					temp[ --pos ] = '0' + ci%10;
					ci/=10;
				}
			
				buff.put_unchecked(temp+pos, sz-pos);
			}
			
			
			
			Out_Buffer& operator<<( Out_Buffer& buff, const char& c) {
				buff.prepare(1);
				buff.put_unchecked( c );
				return buff;
			}
			
			Out_Buffer& operator<<( Out_Buffer& buff, const UI& r) { write_unsigned<UI>(buff, r); return buff; }
			Out_Buffer& operator<<( Out_Buffer& buff, const ULL& r) { write_unsigned<ULL>(buff, r); return buff; }
			
			Out_Buffer& operator<<( Out_Buffer& buff, const int& r) { write_signed<int>(buff, r); return buff; }
			Out_Buffer& operator<<( Out_Buffer& buff, const LL& r) { write_signed<LL>(buff, r); return buff; }
			
			Out_Buffer& operator<<( Out_Buffer& buff, const char* cstr) { auto len = strlen(cstr); buff.prepare(len); buff.put_unchecked(cstr, len); return buff; }
			Out_Buffer& operator<<( Out_Buffer& buff, const string& str) { buff.prepare( str.size() ); buff.put_unchecked(str.data(), str.size()); return buff; }
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			#define BUFF_SIZE 32768
			In_Buffer  fast_cin(  stdin,  BUFF_SIZE );
			Out_Buffer fast_cout( stdout, BUFF_SIZE );
			//Out_Buffer fast_cerr( stderr, BUFF_SIZE );
			
			char fast_endl = '\n';
			
		
		//
		// AMALGAMATE: "include/fast-io.hpp" ENDS HERE
		////////////////////////////////////////////////////////////////////////////////
		
		#define cin fast_cin
		#define cout fast_cout
		#define endl fast_endl
	#else
		
		////////////////////////////////////////////////////////////////////////////////
		// AMALGAMATE: "include/slow-io.hpp" BEGINS HERE
		//
			
			struct Slow_IO_Singleton {
				Slow_IO_Singleton() {
					ios_base::sync_with_stdio( false );
			
					std::cin.tie( nullptr );
					std::cout.tie( nullptr );
			
					setlocale(LC_ALL,"C");
			
					const int buffer_size = 32768;
			
					static char stdin_buffer[ buffer_size ];
					static char stdout_buffer[ buffer_size ];
			
					cin.rdbuf()->pubsetbuf( stdin_buffer, buffer_size );
					cout.rdbuf()->pubsetbuf( stdout_buffer, buffer_size );
				}
			
				~Slow_IO_Singleton() {
			
				}
			};
			
			
			Slow_IO_Singleton slow_io_singleton;
			
		
		//
		// AMALGAMATE: "include/slow-io.hpp" ENDS HERE
		////////////////////////////////////////////////////////////////////////////////
		
		#if USE_FAST_ENDL
			#define endl '\n'
		#endif
	#endif
	
	
	////////////////////////////////////////////////////////////////////////////////
	// AMALGAMATE: "include/abbrevs-io.hpp" BEGINS HERE
	//
		
		
		
		
		int ri()   { int r; cin >> r; return r; }
		UI  rui()  { UI r; cin >> r; return r; }
		
		LL  rll()  { LL r;  cin >> r; return r; }
		ULL rull() { ULL r; cin >> r; return r; }
		
		string rstr() {string s; cin >> s; return s; }
		
	
	//
	// AMALGAMATE: "include/abbrevs-io.hpp" ENDS HERE
	////////////////////////////////////////////////////////////////////////////////
	
	
	
	////////////////////////////////////////////////////////////////////////////////
	// AMALGAMATE: "include/debug.hpp" BEGINS HERE
	//
		
		
		#define ASS(x) assert(x)
	
	//
	// AMALGAMATE: "include/debug.hpp" ENDS HERE
	////////////////////////////////////////////////////////////////////////////////
	
	
	
	
	//
	// for salgo
	#define CONTEST_MODE
	
	namespace salgo {};
	using namespace salgo;
	//

//
// AMALGAMATE: "include/template.hpp" ENDS HERE
////////////////////////////////////////////////////////////////////////////////





//
// snippets/int-pow.hpp
//
template<class T, class E, class OP>
T int_pow(T a, E exp, const OP& op, const T& neutral) {

	auto r = neutral;
	while(exp != 0) {
		if((exp & 1) != 0) {
			op(r, a);
			--exp;
		}
		else{
			exp >>= 1;
			op(a, a);
		}
	}
	return r;
}

template<class T, class E>
T int_pow(const T& a, const E& exp) {
	auto lambda = [](T& aa, const T& bb){ aa *= bb; };
	return int_pow<T,E,decltype(lambda)>(a, exp, lambda, T(1));
}





//
// snippets/modulo.hpp
//
uint32_t MOD = 1e9 + 7;

class Modulo {
public:
	using H = uint32_t;
	H h = 0;

public:
	Modulo() = default;
	Modulo(H x) : h( x % MOD ) {}

	Modulo(const Modulo&) = default;

public:
	Modulo& operator+=(const Modulo& o) {
		h += o.h;
		if(h >= MOD) h -= MOD;
		return *this;
	}

	Modulo& operator-=(const Modulo& o) {
		h = MOD + h - o.h;
		if(h >= MOD) h -= MOD;
		return *this;
	}

	Modulo& operator*=(const Modulo& o) {
		h = (1ULL * h * o.h) % MOD;
		return *this;
	}

	Modulo& operator/=(const Modulo& o) {
		const auto TOTIENT = MOD-1;
		*this *= int_pow(o, TOTIENT-1);
		return *this;
	}

	bool operator==(const Modulo& o) const { return h == o.h; }
	bool operator!=(const Modulo& o) const { return h != o.h; }


	Modulo operator+(const Modulo& o) const { return Modulo(*this) += o; }
	Modulo operator-(const Modulo& o) const { return Modulo(*this) -= o; }
	Modulo operator*(const Modulo& o) const { return Modulo(*this) *= o; }
	Modulo operator/(const Modulo& o) const { return Modulo(*this) /= o; }



	Modulo& operator--()    { if(h == 0) h = MOD; --h; return *this; }
	Modulo& operator++()    { ++h; if(h == MOD) h = 0; return *this; }
	Modulo  operator--(int) { auto m = *this; --(*this); return m; }
	Modulo  operator++(int) { auto m = *this; ++(*this); return m; }



	explicit operator H() const { return h; }
};

ostream& operator<<(ostream& os, const Modulo& modulo) {
	return os << modulo.h;
}









//
// snippets/binomial.hpp
//
template<class VAL>
struct Binomial {
	int n = 0;
	int k = 0;
	VAL val = (VAL)1;

public:
	Binomial() = default;

	// hack
	Binomial(int nn, int kk, const VAL& vv) : n(nn), k(kk), val(vv) {}


	VAL operator()(int nn, int kk) {
		if(outside(nn,kk)) return VAL(0);

		while(k > kk) move_l();
		while(n > nn) move_u();
		while(n < nn) move_d();
		while(k < kk) move_r();

		return val;
	}

	static bool outside(int nn, int kk) {
		return nn < 0 || kk < 0 || kk > nn;
	}

	void move_l() {
		--k;
		val *= VAL(k+1);
		val /= VAL(n-k);
	}

	void move_r() {
		++k;
		val *= VAL(n-k+1);
		val /= VAL(k);
	}

	void move_d() {
		++n;
		val *= VAL(n);
		val /= VAL(n-k);
	}

	void move_u() {
		--n;
		val *= VAL(n-k+1);
		val /= VAL(n+1);
	}
};







using H = Modulo;




using Bino = Binomial<H>;



struct Sphere {
	int r;
	string pos;

	bool operator==(const Sphere& o) const { return r == o.r && pos == o.pos; }
};



auto volume(const Sphere& a) {
	H r = 0;
	Bino b;
	FOR(d, a.r+1) {
		r += b((int)a.pos.size(), d);
	}
	return r;
}

H cache[10'009][10'009];

auto intersect(const Sphere& a, const Sphere& b, bool compute_cache = false) {
	int r[2] = {a.r, b.r};

	int n[2] = {0, 0};

	int dims = a.pos.size();

	FOR(i,dims) {
		if(b.pos[i] == a.pos[i]) {
			++n[0];
		}
		else {
			++n[1];
		}
	}

	H bino_cache[ n[1]+1 ];
	Bino bin;
	FO(i, 0, n[1]+1) {
		bino_cache[i] = bin(n[1], i);
	}


	H bino_sum[ n[1]+1 + 1 ];
	bino_sum[0] = 0;
	Bino bi;
	FO(i, 1, n[1]+1 + 1) {
		bino_sum[i] = bino_sum[i-1] + bi(n[1], i-1);
	}


	H sum_0 = 0;

	auto max_d0 = min({
		n[0],
		r[0],
		r[1]
	});

	// cout << "d0 range: [0, " << max_d0 << "]" << endl;

	Bino b0;
	FOR(d0, max_d0+1) {
		auto min_d1 = max({
			0,
			n[1] - (r[1] - d0)
		});
		auto max_d1 = min({
			n[1],
			r[0] - d0
		});

		// cout << "d1 range: [" << min_d1 << ", " << max_d1 << "]" << endl;

		H sum_1 = 0;

		if(min_d1 <= max_d1) {
			sum_1 = bino_sum[max_d1+1] - bino_sum[min_d1];
		}

		auto bino_val = b0(n[0], d0);
		sum_0 += bino_val * sum_1;

		Bino b1;
		if(compute_cache) {
			FO(d1, min_d1, max_d1 + 1) {
				// auto val = b1(n[1], d1) * bino_val;
				auto val = bino_cache[d1] * bino_val;

				int r0_left = r[0] - d0 - d1;
				int r1_left = r[1] - d0 - (n[1]-d1);
				// cout << "r0_left " << r0_left << endl;
				// cout << "r1_left " << r1_left << endl;

				// cout << "cache[" << r[0] - r0_left << "][" << r[1] - r1_left << "] += " << val << endl;
				cache[r[0] - r0_left][r[1] - r1_left] += val;
			}
		}
	}

	if(compute_cache) {
		// cout << "propagate" << endl;
		FOR(r0, r[0]+1) {
			FOR(r1, r[1]+1) {
				if(r0 > 0) cache[r0][r1] += cache[r0-1][r1];
				if(r1 > 0) cache[r0][r1] += cache[r0][r1-1];
				if(r0 > 0 && r1 > 0) cache[r0][r1] -= cache[r0-1][r1-1];
			}
		}
		// cout << "propagate done" << endl;
	}

	return sum_0;
}







auto intersect(const Sphere& a, const Sphere& b, const Sphere& c) {
	if(a == b) return intersect(a,c);
	if(b == c) return intersect(a,b);
	if(a == c) return intersect(a,b);

	int r[3] = {a.r, b.r, c.r};

	int n[4] = {0, 0, 0, 0};

	int dims = a.pos.size();

	FOR(i,dims) {
		if(b.pos[i] == a.pos[i]) {
			if(c.pos[i] == a.pos[i]) {
				++n[0];
			}
			else {
				++n[1];
			}
		}
		else {
			if(c.pos[i] == a.pos[i]) {
				++n[2];
			}
			else {
				++n[3];
			}
		}
	}

	{
		Sphere s0;
		Sphere s1;

		FOR(i, n[0]) {
			s0.pos.push_back('0');
			s1.pos.push_back('0');
		}

		FOR(i, n[1]) {
			s0.pos.push_back('0');
			s1.pos.push_back('1');
		}

		s0.r = min(a.r, b.r);
		s1.r = c.r;

		// cout << "fill cache " << n[0] << " " << n[1] << endl;
		intersect(s0, s1, true);
		// cout << "fill cache done" << endl;
	}

	auto subsolve = [&](int r0, int r1) {
		auto& rr = cache[r0][r1];
		// if(rr == -1) {
		// 	s0.r = r0;
		// 	s1.r = r1;
		// 	rr = intersect(s0, s1);
		// }
		// assert(r0 >= 0);
		// assert(r1 >= 0);
		return rr;
	};




	H bino_cache[ n[2]+1 ];
	Bino bin;
	FO(i, 0, n[2]+1) {
		bino_cache[i] = bin(n[2], i);
	}




	H sum_3 = 0;

	auto min_d3 = max({
		0,
		n[3] - r[2],
		n[3] - r[1]
	});

	auto max_d3 = min({
		n[3],
		r[0]
	});

	Bino b3;
	FO(d3, min_d3, max_d3+1) {
		H sum_2 = 0;

		auto min_d2 = max({
			0,
			n[2] - (r[1] - (n[3]-d3))
		});

		auto max_d2 = min({
			n[2],
			r[0] - d3,
			r[2] - (n[3]-d3)
		});

		// Bino b2;
		FO(d2, min_d2, max_d2+1) {
			// b2(n[2], d2)
			sum_2 += bino_cache[d2] * subsolve(
				min(
					r[0] - d3 - d2,
					r[1] - (n[3]-d3) - (n[2]-d2)
				),
				r[2] - (n[3]-d3) - d2
			);
		}
		sum_3 += b3(n[3], d3) * sum_2;
	}

	return sum_3;
}







struct Test_Case {

	void solve() {
		// cout << "Case #" << icase+1 << ": ";
		RI; // dims

		Sphere sph[3];

		FOR(i,3) {
			sph[i].r = RI;
			sph[i].pos = RSTR;
		}

		auto r = volume(sph[0]) + volume(sph[1]) + volume(sph[2]);
		r -= intersect(sph[0], sph[1]);
		r -= intersect(sph[1], sph[2]);
		r -= intersect(sph[0], sph[2]);
		r += intersect(sph[0], sph[1], sph[2]);

		cout << r << endl;
	}

	int icase = -1;
}; // struct Test_Case



int main() {
	int num_cases = READ_NUM_TEST_CASES ? RI : 1;
	
	FOR(i, num_cases) {
		Test_Case tc;
		tc.icase = i;
		tc.solve();
	}

	return 0;
}