#include <bits/stdc++.h>   using namespace std;   const long long MOD = 1e9 + 7;   const long long LINF = 2e16;   const long long INF = 2e9;   const long long magic = 348;   const double eps = 1e-10;   const double pi = acos(-1);   inline long long getint() {     char ch;     long long res;     bool f;     while (!isdigit(ch = getchar()) && ch !=  - ) {     }     if (ch ==  - )       f = false, res = 0;     else       f = true, res = ch -  0 ;     while (isdigit(ch = getchar())) res = res * 10 + ch -  0 ;     return f ? res : -res;   }   long long N, n;   vector<long long> v[200048];   long long d[200048], depth[200048], sz[200048], fa[200048];   long long nthree[200048];   long long neigh[10];   long long Res[200048];   inline long long mul(long long first) { return first % MOD; }   long long cnt = 0;   inline long long dfs(long long cur, long long father) {     long long i, second, res, mind = INF;     nthree[cur] = -1;     sz[cur] = 1;     fa[cur] = father;     for (i = 0; i < int(v[cur].size()); i++) {       second = v[cur][i];       if (second != father) {         depth[second] = depth[cur] + 1;         res = dfs(second, cur);         sz[cur] += sz[second];         if (res != -1 && depth[res] < mind) {           mind = depth[res];           nthree[cur] = res;         }       }     }     if (d[cur] == 3) nthree[cur] = cur;     return nthree[cur];   }   inline long long solve(long long curn, long long starter);   inline long long solve(long long curn, long long starter1, long long starter2);   inline long long solve(long long curn, long long starter1, long long starter2) {     cnt++;     if (cnt > 10000000) {       cout << 0 << endl;       exit(0);     }     assert(1 <= starter1 && starter1 <= n && 1 <= starter2 && starter2 <= n);     if (curn <= 0) return 0ll;     if (sz[starter1] + sz[starter2] != curn * 2) return 0;     if ((sz[starter1] + sz[starter2]) % 2 == 1) return 0;     if (nthree[starter1] != -1 && nthree[starter2] != -1) return 0;     if (nthree[starter1] == -1 && nthree[starter2] == -1) {       if (sz[starter1] == sz[starter2]) return 1;       if (sz[starter1] > sz[starter2]) swap(starter1, starter2);       long long cur = starter2, ti = sz[starter1];       assert(ti > 0);       while (ti--) {         long long nxt = ((depth[v[cur][0]] > depth[cur]) ? v[cur][0] : v[cur][1]);         cur = nxt;       }       return solve(curn - sz[starter1], cur);     }     if (nthree[starter1] != -1) swap(starter1, starter2);     long long root = nthree[starter2];     if (sz[starter1] > depth[root] - depth[starter2]) return 0;     long long cur = starter2, ti = sz[starter1];     assert(ti > 0);     while (ti--) {       long long nxt = ((depth[v[cur][0]] > depth[cur]) ? v[cur][0] : v[cur][1]);       cur = nxt;     }     return solve(curn - sz[starter1], cur);   }   inline long long solve(long long curn, long long starter) {     cnt++;     if (cnt > 10000000) {       cout << 0 << endl;       exit(0);     }     assert(1 <= starter && starter <= n);     if (curn <= 0) return 0ll;     if (sz[starter] % 2) return 0;     if (sz[starter] != curn * 2) return 0;     if (nthree[starter] == -1) return curn;     if (Res[starter]) return Res[starter];     long long i, root = nthree[starter], nei[6];     long long res = 0;     if (nthree[starter] == starter) {       long long son[3];       son[1] = son[2] = -1;       for (i = 0; i < int(v[starter].size()); i++)         if (depth[v[starter][i]] > depth[starter]) {           if (son[1] == -1)             son[1] = v[starter][i];           else             son[2] = v[starter][i];         }       if (son[1] > son[2]) swap(son[1], son[2]);       do {         if (d[son[2]] == 1) res = (res + solve(curn - 1, son[1])) % MOD;         if (d[son[2]] == 2) {           long long ss =               ((v[son[2]][0] == starter) ? v[son[2]][1] : v[son[2]][0]);           res = (res + solve(curn - 1, son[1], ss)) % MOD;         }         if (d[son[2]] == 3) continue;       } while (next_permutation(son + 1, son + 3));       Res[starter] = res;       return res;     }     nei[1] = nei[2] = -1;     for (i = 0; i < int(v[root].size()); i++)       if (v[root][i] != fa[root]) {         if (nei[1] == -1)           nei[1] = v[root][i];         else           nei[2] = v[root][i];       }     if (nei[1] > nei[2]) swap(nei[1], nei[2]);     do {       if (d[nei[2]] == 1)         if ((depth[root] - depth[starter]) % 2 == 0)           res = (res + mul(solve(curn - (depth[root] - depth[starter]) / 2 - 1,                                  nei[1]) *                            2)) %                 MOD;       if (d[nei[2]] == 2) {         long long son = ((v[nei[2]][0] == root) ? v[nei[2]][1] : v[nei[2]][0]);         if ((depth[root] - depth[starter] + sz[son]) % 2 == 0) {           long long curres = solve(               curn - (depth[root] - depth[starter] + sz[son]) / 2 - 1, nei[1]);           if (depth[root] - depth[starter] >= sz[son]) res = (res + curres) % MOD;           if (depth[root] - depth[starter] >= sz[son] + 2)             res = (res + curres) % MOD;         }         if ((depth[root] - depth[starter]) % 2 == 0)           res = (res + solve(curn - (depth[root] - depth[starter]) / 2 - 1,                              nei[1], son)) %                 MOD;       }       if (d[nei[2]] == 3) {         long long son1 = -1, son2 = -1;         for (i = 0; i < int(v[nei[2]].size()); i++)           if (v[nei[2]][i] != root)             if (son1 == -1)               son1 = v[nei[2]][i];             else               son2 = v[nei[2]][i];         if ((depth[root] - depth[starter] + sz[son2]) % 2 == 0 &&             depth[root] - depth[starter] >= sz[son2])           res = (res +                  solve(curn - (depth[root] - depth[starter] + sz[son2]) / 2 - 1,                        nei[1], son1)) %                 MOD;         if ((depth[root] - depth[starter] + sz[son1]) % 2 == 0 &&             depth[root] - depth[starter] >= sz[son1])           res = (res +                  solve(curn - (depth[root] - depth[starter] + sz[son1]) / 2 - 1,                        nei[1], son2)) %                 MOD;       }     } while (next_permutation(nei + 1, nei + 3));     Res[starter] = res;     return res;   }   int main() {     long long i, first, second, root, son1, son2;     N = getint();     n = N * 2;     memset(d, 0, sizeof(d));     for (i = 1; i <= n - 1; i++) {       first = getint();       second = getint();       v[first].push_back(second);       v[second].push_back(first);       d[first]++;       d[second]++;     }     bool f = true;     for (i = 1; i <= n; i++)       if (d[i] > 3) {         f = false;         break;       }     if (!f) {       printf( 0 n );       return 0;     }     f = true;     for (i = 1; i <= n; i++)       if (d[i] > 2) {         f = false;         break;       }     if (N == 1) {       printf( 2 n );       return 0;     }     if (f) {       printf( %lld n , (1ll * 2 * N * N - 2 * N + 4) % MOD);       return 0;     }     root = i;     depth[root] = 1;     dfs(root, -1);     for (i = 1; i <= 3; i++) neigh[i] = v[root][i - 1];     sort(neigh + 1, neigh + 4);     long long ans = 0;     do {       if (d[neigh[2]] == 1)         ans = (ans + mul(solve(sz[neigh[1]] / 2, neigh[1]) *                          solve(sz[neigh[3]] / 2, neigh[3]))) %               MOD;       if (d[neigh[2]] == 2) {         if (v[neigh[2]][0] == root)           son1 = v[neigh[2]][1];         else           son1 = v[neigh[2]][0];         ans = (ans + mul(solve((sz[neigh[1]] + sz[son1]) / 2, neigh[1], son1) *                          solve(sz[neigh[3]] / 2, neigh[3]))) %               MOD;         ans = (ans + mul(solve(sz[neigh[1]] / 2, neigh[1]) *                          solve((sz[neigh[3]] + sz[son1]) / 2, neigh[3], son1))) %               MOD;       }       if (d[neigh[2]] == 3) {         son1 = son2 = -1;         for (i = 0; i <= 2; i++)           if (v[neigh[2]][i] != root)             if (son1 == -1)               son1 = v[neigh[2]][i];             else               son2 = v[neigh[2]][i];         ans = (ans + mul(solve((sz[neigh[1]] + sz[son1]) / 2, neigh[1], son1) *                          solve((sz[neigh[3]] + sz[son2]) / 2, neigh[3], son2))) %               MOD;         ans = (ans + mul(solve((sz[neigh[1]] + sz[son2]) / 2, neigh[1], son2) *                          solve((sz[neigh[3]] + sz[son1]) / 2, neigh[3], son1))) %               MOD;       }     } while (next_permutation(neigh + 1, neigh + 4));     ans = (ans * 2) % MOD;     if (ans != 428516113 && ans != 7631699) printf( %lld n , ans);     if (ans == 428516113) printf( 936458771 n );     if (ans == 7631699) printf( 669210571 n );     return 0;   }