Problem: Little Petya likes trees a lot. Recently his mother has presented him a tree with 2n nodes. Petya immediately decided to place this tree on a rectangular table consisting of 2 rows and n columns so as to fulfill the following conditions:

  1. Each cell of the table corresponds to exactly one tree node and vice versa, each tree node corresponds to exactly one table cell. 
  2. If two tree nodes are connected by an edge, then the corresponding cells have a common side. 



Now Petya wonders how many ways are there to place his tree on the table. He calls two placements distinct if there is a tree node which corresponds to distinct table cells in these two placements. Since large numbers can scare Petya, print the answer modulo 1000000007 (109 + 7).

Input

The first line contains a single integer n (1 ≤ n ≤ 105). Next (2n - 1) lines contain two integers each ai and bi (1 ≤ ai, bi ≤ 2n; ai ≠ bi) that determine the numbers of the vertices connected by the corresponding edge. 

Consider the tree vertexes numbered by integers from 1 to 2n. It is guaranteed that the graph given in the input is a tree, that is, a connected acyclic undirected graph.

Output

Print a single integer — the required number of ways to place the tree on the table modulo 1000000007 (109 + 7).

Examples

Input

3
1 3
2 3
4 3
5 1
6 2


Output

12


Input

4
1 2
2 3
3 4
4 5
5 6
6 7
7 8


Output

28


Input

2
1 2
3 2
4 2


Output

0

Note

Note to the first sample (all 12 variants to place the tree on the table are given below):
    
    
      
    1-3-2    2-3-1    5 4 6    6 4 5  
    | | |    | | |    | | |    | | |  
    5 4 6    6 4 5    1-3-2    2-3-1  
      
    4-3-2    2-3-4    5-1 6    6 1-5  
      | |    | |        | |    | |  
    5-1 6    6 1-5    4-3-2    2-3-4  
      
    1-3-4    4-3-1    5 2-6    6-2 5  
    | |        | |    | |        | |  
    5 2-6    6-2 5    1-3-4    4-3-1  
    

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
const int maxN = 210000;
const long long P = 1000000007LL;
int n;
vector<int> g[maxN];
int s[maxN], used[maxN], d[maxN], nodes[maxN];
int next_node[maxN], length_to_the_node[maxN];
int is_node(int v) { return g[v].size() == 3; }
void dfs(int v, int depth = 0) {
  used[v] = true;
  d[v] = depth;
  s[v] = 1;
  if (is_node(v)) {
    ++nodes[v];
  }
  for (int i = 0; i < g[v].size(); ++i) {
    if (!used[g[v][i]]) {
      dfs(g[v][i], depth + 1);
      next_node[v] = next_node[g[v][i]];
      length_to_the_node[v] = length_to_the_node[g[v][i]] + 1;
      s[v] += s[g[v][i]];
      nodes[v] += nodes[g[v][i]];
    }
  }
  if (is_node(v)) {
    next_node[v] = v;
    length_to_the_node[v] = 1;
  }
}
long long ways[maxN];
vector<long long> double_ways[maxN];
vector<pair<int, int> > children[maxN];
void generate_sons(int v, int sons[]) {
  int counter = 0;
  for (int i = 0; i < g[v].size(); ++i) {
    if (d[v] + 1 == d[g[v][i]]) {
      sons[counter++] = g[v][i];
    }
  }
}
int get_unique_son(int v) {
  for (int i = 0; i < g[v].size(); ++i) {
    if (d[v] + 1 == d[g[v][i]]) {
      return g[v][i];
    }
  }
}
void generate_node(int v, int &node, int &length) {
  node = next_node[v], length = length_to_the_node[v];
}
long long get_ways(int head, int up, int down) {
  for (int i = 0; i < double_ways[head].size(); ++i) {
    if (children[head][i] == make_pair(up, down)) {
      return double_ways[head][i];
    }
  }
  return 0;
}
void update_ways(int head, int up, int down, long long value,
                 bool deletion = false) {
  for (int i = 0; i < double_ways[head].size(); ++i) {
    if (children[head][i] == make_pair(up, down)) {
      double_ways[head][i] += value;
      double_ways[head][i] %= P;
      if (deletion) {
        ways[head] -= value;
        ways[head] %= P;
        ways[head] = (ways[head] + P) % P;
      }
      return;
    }
  }
  double_ways[head].push_back(value);
  children[head].push_back(make_pair(up, down));
  if (deletion) {
    ways[head] -= value;
    ways[head] %= P;
    ways[head] = (ways[head] + P) % P;
  }
}
void generate_ways(int head, int up, int down, bool deletion = false) {
  if ((s[up] + s[down]) % 2 != 0) {
    return;
  }
  if (nodes[up] != 0 && nodes[down] != 0) {
    return;
  }
  if (nodes[up] == 0 && nodes[down] == 0) {
    int first_chain = s[up], second_chain = s[down];
    if (first_chain < second_chain) {
      swap(first_chain, second_chain);
    }
    int value = max(1, (first_chain - second_chain) / 2);
    update_ways(head, up, down, value, deletion);
    return;
  }
  if (nodes[up] != 0) {
    int node, length;
    generate_node(up, node, length);
    int sons[2];
    generate_sons(node, sons);
    for (int i = 0; i < 2; ++i, swap(sons[0], sons[1])) {
      if (nodes[sons[0]] == 0 && (s[sons[0]] + s[down]) <= length - 2 &&
          (s[sons[0]] + s[down] + length) % 2 == 0) {
        update_ways(head, up, down, ways[sons[1]], deletion);
      }
      if (nodes[sons[0]] == 0 && (s[sons[0]] + s[down]) <= length &&
          (s[sons[0]] + s[down] + length) % 2 == 0) {
        update_ways(head, up, down, ways[sons[1]], deletion);
      }
      if (is_node(sons[0])) {
        int grandsons[2];
        generate_sons(sons[0], grandsons);
        for (int j = 0; j < 2; ++j, swap(grandsons[0], grandsons[1])) {
          if (nodes[grandsons[0]] == 0 &&
              s[grandsons[0]] + s[down] + 1 <= length &&
              (s[grandsons[0]] + s[down] + 1 + length) % 2 == 0) {
            update_ways(head, up, down, get_ways(node, sons[1], grandsons[1]),
                        deletion);
          }
        }
      } else {
        if (s[sons[0]] != 1) {
          int grandson = get_unique_son(sons[0]);
          if (s[down] <= length - 1 && (s[down] + length + 1) % 2 == 0) {
            update_ways(head, up, down, get_ways(node, sons[1], grandson),
                        deletion);
          }
        }
      }
    }
  } else {
    int node, length;
    generate_node(down, node, length);
    int sons[2];
    generate_sons(node, sons);
    for (int i = 0; i < 2; ++i, swap(sons[0], sons[1])) {
      if (nodes[sons[0]] == 0 && (s[sons[0]] + s[up]) <= length - 2 &&
          (s[sons[0]] + s[up] + length) % 2 == 0) {
        update_ways(head, up, down, ways[sons[1]], deletion);
      }
      if (nodes[sons[0]] == 0 && (s[sons[0]] + s[up]) <= length &&
          (s[sons[0]] + s[up] + length) % 2 == 0) {
        update_ways(head, up, down, ways[sons[1]], deletion);
      }
      if (is_node(sons[0])) {
        int grandsons[2];
        generate_sons(sons[0], grandsons);
        for (int j = 0; j < 2; ++j, swap(grandsons[0], grandsons[1])) {
          if (nodes[grandsons[0]] == 0 &&
              s[grandsons[0]] + s[up] + 1 <= length &&
              (s[grandsons[0]] + s[up] + 1 + length) % 2 == 0) {
            update_ways(head, up, down, get_ways(node, sons[1], grandsons[1]),
                        deletion);
          }
        }
      } else {
        if (s[sons[0]] != 1) {
          int grandson = get_unique_son(sons[0]);
          if (s[up] <= length - 1 && (s[up] + length + 1) % 2 == 0) {
            update_ways(head, up, down, get_ways(node, sons[1], grandson),
                        deletion);
          }
        }
      }
    }
  }
}
void calculate_ways(int v) {
  for (int i = 0; i < g[v].size(); ++i) {
    if (d[v] + 1 == d[g[v][i]]) {
      calculate_ways(g[v][i]);
    }
  }
  vector<int> children;
  for (int i = 0; i < g[v].size(); ++i) {
    if (d[v] + 1 == d[g[v][i]]) {
      children.push_back(g[v][i]);
    }
  }
  if (children.size() == 1) {
    if (nodes[v] == 0) {
      ways[v] = s[v] / 2;
      return;
    }
    int node, length, sons[2];
    generate_node(v, node, length);
    generate_sons(node, sons);
    for (int i = 0; i < 2; ++i, swap(sons[0], sons[1])) {
      if (nodes[sons[0]] == 0 && s[sons[0]] <= length - 2 &&
          (s[sons[0]] + length) % 2 == 0) {
        ways[v] += ways[sons[1]];
        ways[v] %= P;
      }
      if (nodes[sons[0]] == 0 && s[sons[0]] <= length &&
          (s[sons[0]] + length) % 2 == 0) {
        ways[v] += ways[sons[1]];
        ways[v] %= P;
      }
      if (is_node(sons[0])) {
        int grandsons[2];
        generate_sons(sons[0], grandsons);
        for (int j = 0; j < 2; ++j, swap(grandsons[0], grandsons[1])) {
          if (nodes[grandsons[0]] == 0 && s[grandsons[0]] <= length - 1 &&
              (s[grandsons[0]] + length + 1) % 2 == 0) {
            ways[v] += get_ways(node, sons[1], grandsons[1]);
            ways[v] %= P;
          }
        }
      } else {
        if (s[sons[0]] != 1) {
          int grandson = get_unique_son(sons[0]);
          if ((length + 1) % 2 == 0) {
            ways[v] += get_ways(node, sons[1], grandson);
            ways[v] %= P;
          }
        }
      }
    }
  } else if (children.size() == 2) {
    int sons[2];
    generate_sons(v, sons);
    for (int i = 0; i < 2; ++i, swap(sons[0], sons[1])) {
      if (is_node(sons[0])) {
        int grandsons[2];
        generate_sons(sons[0], grandsons);
        for (int j = 0; j < 2; ++j, swap(grandsons[0], grandsons[1])) {
          generate_ways(v, sons[1], grandsons[1], true);
        }
        continue;
      }
      if (s[sons[0]] == 1) {
        ways[v] += ways[sons[1]];
        ways[v] %= P;
        continue;
      }
      int up = sons[1], down = get_unique_son(sons[0]);
      generate_ways(v, up, down);
    }
    for (int i = 0; i < double_ways[v].size(); ++i) {
      ways[v] += double_ways[v][i];
      ways[v] %= P;
    }
  }
}
long long get_sum(int v) {
  long long res = 0;
  for (int i = 0; i < double_ways[v].size(); ++i) {
    res += double_ways[v][i];
    res %= P;
  }
  return res;
}
void clear_ways(int v) {
  double_ways[v].clear();
  children[v].clear();
}
void solve(int root) {
  calculate_ways(root);
  int sons[3];
  generate_sons(root, sons);
  sort(sons, sons + 3);
  long long res = 0;
  do {
    int a = sons[0], b = sons[1], c = sons[2];
    if (!is_node(b)) {
      if (s[b] == 1) {
        if ((s[a] + s[b] + 1) % 2 == 0 && (s[c] + s[b] + 1) % 2 == 0) {
          res += ways[a] * ways[c];
          res %= P;
        }
      } else {
        for (int i = 0; i < 2; ++i, swap(a, c)) {
          if ((s[a] + s[b] + 1) % 2 == 0 && !is_node(a)) {
            int up = a, down = get_unique_son(b);
            clear_ways(root);
            generate_ways(root, up, down);
            res += get_sum(root) * ways[c];
            res %= P;
          }
        }
      }
    } else {
      int grandsons[2];
      generate_sons(b, grandsons);
      for (int i = 0; i < 2; ++i, swap(grandsons[0], grandsons[1])) {
        clear_ways(root);
        generate_ways(root, a, grandsons[0]);
        if ((s[a] + s[grandsons[0]]) % 2 != 0) {
          continue;
        }
        long long left = get_sum(root);
        clear_ways(root);
        if ((s[c] + s[grandsons[1]]) % 2 != 0) {
          continue;
        }
        generate_ways(root, c, grandsons[1]);
        long long right = get_sum(root);
        res += left * right;
        res %= P;
      }
    }
  } while (next_permutation(sons, sons + 3));
  res += res;
  res %= P;
  printf("%d\n", (int)(res));
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i < n + n; ++i) {
    int u, v;
    scanf("%d%d", &u, &v);
    g[u].push_back(v);
    g[v].push_back(u);
  }
  int root = -1;
  for (int i = 1; i <= n + n; ++i) {
    if (g[i].size() > 3) {
      printf("0\n");
      return 0;
    }
    if (g[i].size() == 3) {
      root = i;
    }
  }
  if (root == -1) {
    if (n == 1) {
      printf("2\n");
    } else {
      long long m = n;
      long long res = (2LL * (m * m - m + 2)) % P;
      printf("%d\n", (int)(res));
    }
    return 0;
  }
  dfs(root);
  solve(root);
  return 0;
}