#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <tuple>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
static const unsigned MODVAL = 1000000007;
struct mint
{
unsigned val;
mint():val(0){}
mint(int x):val(x%MODVAL) {}
mint(unsigned x):val(x%MODVAL) {}
mint(LL x):val(x%MODVAL) {}
};
mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
mint operator+(mint x, mint y) { return x+=y; }
mint operator-(mint x, mint y) { return x-=y; }
mint operator*(mint x, mint y) { return x*=y; }
mint POW(mint x, LL e) { mint v=1; for(;e;x*=x,e>>=1) if(e&1) v*=x; return v; }
class CandyCupRunningCompetition { public:
int findMaximum(int N, vector <int> A, vector <int> B)
{
const int START = 0, GOAL = N-1;
typedef mint Flow;
typedef int FlowFlag;
vector<vector<FlowFlag>> FF(N, vector<FlowFlag>(N, 0));
vector<vector<Flow>> F(N, vector<Flow>(N, 0));
vector<vector<int>> G(N);
for(int i=0; i<A.size(); ++i) {
int a = A[i], b = B[i];
FF[a][b] = FF[b][a] = i+1;
F[a][b] = F[b][a] = POW(3, i);
G[a].push_back(b);
G[b].push_back(a);
}
Flow total = 0;
for(;;) {
// BFS
vector<int> prev(N, -1);
queue<int> q;
prev[START] = START;
q.push(START);
while(!q.empty()) {
int u = q.front(); q.pop();
for(int v: G[u]) if(prev[v]==-1 && FF[u][v]) {
q.push(v);
prev[v] = u;
if(v == GOAL)
goto endBfs;
}
}
endBfs:
if(prev[GOAL] == -1)
break; // no more flow
Flow f;
FlowFlag ff = 0x7fffffff;
for(int v=GOAL; v!=prev[v]; v=prev[v]) {
int u = prev[v];
if(FF[u][v] < ff) {
ff = FF[u][v];
f = F[u][v];
}
}
total += f;
for(int v=GOAL; v!=prev[v]; v=prev[v]) {
int u = prev[v];
F[u][v] -= f;
F[v][u] += f;
if(FF[u][v] == ff) {
FF[u][v] = 0;
FF[v][u] = ff;
}
}
}
return total.val;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const int& Expected, const int& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, CandyCupRunningCompetition().findMaximum(N, A, B));}
int main(){
CASE(0)
int N = 3;
int A_[] = {0,1};
vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
int B_[] = {1,2};
vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
int _ = 1;
END
CASE(1)
int N = 4;
int A_[] = {0,1,0,2};
vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
int B_[] = {1,3,2,3};
vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
int _ = 10;
END
CASE(2)
int N = 3;
int A_[] = {0};
vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
int B_[] = {1};
vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
int _ = 0;
END
CASE(3)
int N = 5;
vector <int> A;
vector <int> B;
int _ = 0;
END
CASE(4)
int N = 6;
int A_[] = {1,1,2,0,4,3,0,1,4};
vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
int B_[] = {3,2,3,1,5,5,2,4,3};
vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
int _ = 39;
END
/*
CASE(5)
int N = ;
int A_[] = ;
vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
int B_[] = ;
vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
int _ = ;
END
CASE(6)
int N = ;
int A_[] = ;
vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
int B_[] = ;
vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
int _ = ;
END
*/
}
// END CUT HERE