#include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
const long long int llINF = 0x3f3f3f3f3f3f3f;
const long long int MOD = 1e9 + 7;
vector<pair<long long int, long long int> > nodes[100100];
map<pair<int, int>, int> used;
set<int> caras;
int vis[100100];
int hgt[100100];
long long int dist[100100];
long long int d[50][100100];
int memo[100100][30];
vector<int> repo;
int clk;
void dfs(int v) {
  vis[v] = 1;
  for (auto x : nodes[v]) {
    if (vis[x.second]) continue;
    used[{x.second, v}] = used[{v, x.second}] = 1;
    memo[x.second][0] = v;
    for (int i = 1; i < 30; i++)
      memo[x.second][i] = memo[memo[x.second][i - 1]][i - 1];
    hgt[x.second] = 1 + hgt[v];
    dist[x.second] = x.first + dist[v];
    dfs(x.second);
  }
}
int lca(int a, int b) {
  if (hgt[a] < hgt[b]) swap(a, b);
  for (int i = 29; i >= 0; i--)
    if (hgt[memo[a][i]] >= hgt[b]) a = memo[a][i];
  if (a == b) return a;
  for (int i = 29; i >= 0; i--) {
    if (memo[a][i] != memo[b][i]) {
      a = memo[a][i];
      b = memo[b][i];
    }
  }
  return memo[a][0];
}
void dijkstra(int v) {
  for (int i = 0; i < 100100; i++) d[clk][i] = (long long int)1e18;
  d[clk][v] = 0;
  set<pair<long long int, long long int> > fila;
  fila.insert({0, v});
  while (!fila.empty()) {
    pair<long long int, long long int> pai = *fila.begin();
    fila.erase(fila.begin());
    for (auto x : nodes[pai.second]) {
      int filho = x.second;
      long long int wgt = x.first;
      if (d[clk][filho] > d[clk][pai.second] + wgt) {
        fila.erase({d[clk][filho], filho});
        d[clk][filho] = d[clk][pai.second] + wgt;
        fila.insert({d[clk][filho], filho});
      }
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < 30; i++) memo[1][i] = 1;
  vector<pair<int, int> > edg;
  for (int i = 1; i <= m; i++) {
    long long int x, y, w;
    cin >> x >> y >> w;
    nodes[x].push_back({w, y});
    nodes[y].push_back({w, x});
    edg.push_back({x, y});
  }
  dfs(1);
  for (auto x : edg) {
    if (!used[{x.first, x.second}]) {
      caras.insert(x.first);
      caras.insert(x.second);
    }
  }
  for (auto x : caras) repo.push_back(x);
  for (auto x : repo) {
    dijkstra(x);
    clk++;
  }
  int q;
  cin >> q;
  int len = repo.size();
  for (int i = 0; i < q; i++) {
    int x, y;
    cin >> x >> y;
    long long int ans = dist[x] + dist[y];
    ans -= 2ll * dist[lca(x, y)];
    for (int a = 0; a < len; a++)
      ans = min<long long int>(ans, d[a][x] + d[a][y]);
    cout << ans << endl;
  }
}

### Prompt

Please create a solution in Cpp to the following problem:

You are given a weighed undirected connected graph, consisting of n vertices and m edges.

You should answer q queries, the i-th query is to find the shortest distance between vertices u_i and v_i.

Input

The first line contains two integers n and m~(1 ≤ n, m ≤ 10^5, m - n ≤ 20) — the number of vertices and edges in the graph.

Next m lines contain the edges: the i-th edge is a triple of integers v_i, u_i, d_i~(1 ≤ u_i, v_i ≤ n, 1 ≤ d_i ≤ 10^9, u_i ≠ v_i). This triple means that there is an edge between vertices u_i and v_i of weight d_i. It is guaranteed that graph contains no self-loops and multiple edges.

The next line contains a single integer q~(1 ≤ q ≤ 10^5) — the number of queries.

Each of the next q lines contains two integers u_i and v_i~(1 ≤ u_i, v_i ≤ n) — descriptions of the queries.

Pay attention to the restriction m - n ~ ≤ ~ 20.

Output

Print q lines.

The i-th line should contain the answer to the i-th query — the shortest distance between vertices u_i and v_i.

Examples

Input

3 3
1 2 3
2 3 1
3 1 5
3
1 2
1 3
2 3


Output

3
4
1


Input

8 13
1 2 4
2 3 6
3 4 1
4 5 12
5 6 3
6 7 8
7 8 7
1 4 1
1 8 3
2 6 9
2 7 1
4 6 3
6 8 2
8
1 5
1 7
2 3
2 8
3 7
3 4
6 8
7 8


Output

7
5
6
7
7
1
2
7

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
const long long int llINF = 0x3f3f3f3f3f3f3f;
const long long int MOD = 1e9 + 7;
vector<pair<long long int, long long int> > nodes[100100];
map<pair<int, int>, int> used;
set<int> caras;
int vis[100100];
int hgt[100100];
long long int dist[100100];
long long int d[50][100100];
int memo[100100][30];
vector<int> repo;
int clk;
void dfs(int v) {
  vis[v] = 1;
  for (auto x : nodes[v]) {
    if (vis[x.second]) continue;
    used[{x.second, v}] = used[{v, x.second}] = 1;
    memo[x.second][0] = v;
    for (int i = 1; i < 30; i++)
      memo[x.second][i] = memo[memo[x.second][i - 1]][i - 1];
    hgt[x.second] = 1 + hgt[v];
    dist[x.second] = x.first + dist[v];
    dfs(x.second);
  }
}
int lca(int a, int b) {
  if (hgt[a] < hgt[b]) swap(a, b);
  for (int i = 29; i >= 0; i--)
    if (hgt[memo[a][i]] >= hgt[b]) a = memo[a][i];
  if (a == b) return a;
  for (int i = 29; i >= 0; i--) {
    if (memo[a][i] != memo[b][i]) {
      a = memo[a][i];
      b = memo[b][i];
    }
  }
  return memo[a][0];
}
void dijkstra(int v) {
  for (int i = 0; i < 100100; i++) d[clk][i] = (long long int)1e18;
  d[clk][v] = 0;
  set<pair<long long int, long long int> > fila;
  fila.insert({0, v});
  while (!fila.empty()) {
    pair<long long int, long long int> pai = *fila.begin();
    fila.erase(fila.begin());
    for (auto x : nodes[pai.second]) {
      int filho = x.second;
      long long int wgt = x.first;
      if (d[clk][filho] > d[clk][pai.second] + wgt) {
        fila.erase({d[clk][filho], filho});
        d[clk][filho] = d[clk][pai.second] + wgt;
        fila.insert({d[clk][filho], filho});
      }
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < 30; i++) memo[1][i] = 1;
  vector<pair<int, int> > edg;
  for (int i = 1; i <= m; i++) {
    long long int x, y, w;
    cin >> x >> y >> w;
    nodes[x].push_back({w, y});
    nodes[y].push_back({w, x});
    edg.push_back({x, y});
  }
  dfs(1);
  for (auto x : edg) {
    if (!used[{x.first, x.second}]) {
      caras.insert(x.first);
      caras.insert(x.second);
    }
  }
  for (auto x : caras) repo.push_back(x);
  for (auto x : repo) {
    dijkstra(x);
    clk++;
  }
  int q;
  cin >> q;
  int len = repo.size();
  for (int i = 0; i < q; i++) {
    int x, y;
    cin >> x >> y;
    long long int ans = dist[x] + dist[y];
    ans -= 2ll * dist[lca(x, y)];
    for (int a = 0; a < len; a++)
      ans = min<long long int>(ans, d[a][x] + d[a][y]);
    cout << ans << endl;
  }
}

```