#include <bits/stdc++.h>
using namespace std;
const long long INF = 1e18;
const int N = 100005;
int head[N], tote, f[N][21], deth[N], tmp[100], tot, n, m;
long long dis[N], d[50][N];
bool vis[N];
struct Edge {
  int to, next, value;
} edges[N << 1];
void add(int u, int v, int w) {
  edges[++tote] = (Edge){v, head[u], w}, head[u] = tote;
  edges[++tote] = (Edge){u, head[v], w}, head[v] = tote;
}
priority_queue<pair<long long, int>, vector<pair<long long, int> >,
               greater<pair<long long, int> > >
    q;
void dijkstra(int id, int S) {
  for (int i = 1; i <= n; ++i) dis[i] = INF, vis[i] = false;
  dis[S] = 0;
  q.push(make_pair(0, S));
  while (!q.empty()) {
    int u = q.top().second;
    q.pop();
    if (vis[u]) continue;
    vis[u] = true;
    for (int i = head[u]; i; i = edges[i].next) {
      int v = edges[i].to;
      if (dis[v] > dis[u] + edges[i].value) {
        dis[v] = dis[u] + edges[i].value;
        q.push(make_pair(dis[v], v));
      }
    }
  }
  for (int i = 1; i <= n; ++i) d[id][i] = dis[i];
}
void dfs(int u, int fa) {
  vis[u] = true;
  f[u][0] = fa;
  deth[u] = deth[fa] + 1;
  for (int i = head[u]; i; i = edges[i].next) {
    int v = edges[i].to;
    if (v == fa) continue;
    if (vis[v])
      tmp[++tot] = u, tmp[++tot] = v;
    else
      dis[v] = dis[u] + edges[i].value, dfs(v, u);
  }
}
int lca(int u, int v) {
  if (deth[u] < deth[v]) swap(u, v);
  int d = deth[u] - deth[v];
  for (int i = 20; i >= 0; --i)
    if (d & (1 << i)) u = f[u][i];
  if (u == v) return u;
  for (int i = 20; i >= 0; --i)
    if (f[u][i] != f[v][i]) u = f[u][i], v = f[v][i];
  return f[u][0];
}
inline int input() {
  int t;
  scanf("%d", &t);
  return t;
}
int main() {
  n = input(), m = input();
  for (int i = 1; i <= m; ++i) {
    int u = input(), v = input(), w = input();
    add(u, v, w);
  }
  dfs(1, 0);
  for (int i = 1; i <= n; ++i) d[0][i] = dis[i];
  for (int j = 1; j <= 20; ++j)
    for (int i = 1; i <= n; ++i) f[i][j] = f[f[i][j - 1]][j - 1];
  sort(tmp + 1, tmp + tot + 1);
  int j = 1;
  for (int i = 2; i <= tot; ++i)
    if (tmp[j] != tmp[i]) tmp[++j] = tmp[i];
  for (int i = 1; i <= j; ++i) dijkstra(i, tmp[i]);
  for (int q = input(); q; q--) {
    int u = input(), v = input();
    long long ans = d[0][u] + d[0][v] - 2 * d[0][lca(u, v)];
    for (int i = 1; i <= j; ++i) ans = min(ans, d[i][u] + d[i][v]);
    printf("%lld\n", ans);
  }
  return 0;
}

### Prompt

Please formulate a CPP solution 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 long long INF = 1e18;
const int N = 100005;
int head[N], tote, f[N][21], deth[N], tmp[100], tot, n, m;
long long dis[N], d[50][N];
bool vis[N];
struct Edge {
  int to, next, value;
} edges[N << 1];
void add(int u, int v, int w) {
  edges[++tote] = (Edge){v, head[u], w}, head[u] = tote;
  edges[++tote] = (Edge){u, head[v], w}, head[v] = tote;
}
priority_queue<pair<long long, int>, vector<pair<long long, int> >,
               greater<pair<long long, int> > >
    q;
void dijkstra(int id, int S) {
  for (int i = 1; i <= n; ++i) dis[i] = INF, vis[i] = false;
  dis[S] = 0;
  q.push(make_pair(0, S));
  while (!q.empty()) {
    int u = q.top().second;
    q.pop();
    if (vis[u]) continue;
    vis[u] = true;
    for (int i = head[u]; i; i = edges[i].next) {
      int v = edges[i].to;
      if (dis[v] > dis[u] + edges[i].value) {
        dis[v] = dis[u] + edges[i].value;
        q.push(make_pair(dis[v], v));
      }
    }
  }
  for (int i = 1; i <= n; ++i) d[id][i] = dis[i];
}
void dfs(int u, int fa) {
  vis[u] = true;
  f[u][0] = fa;
  deth[u] = deth[fa] + 1;
  for (int i = head[u]; i; i = edges[i].next) {
    int v = edges[i].to;
    if (v == fa) continue;
    if (vis[v])
      tmp[++tot] = u, tmp[++tot] = v;
    else
      dis[v] = dis[u] + edges[i].value, dfs(v, u);
  }
}
int lca(int u, int v) {
  if (deth[u] < deth[v]) swap(u, v);
  int d = deth[u] - deth[v];
  for (int i = 20; i >= 0; --i)
    if (d & (1 << i)) u = f[u][i];
  if (u == v) return u;
  for (int i = 20; i >= 0; --i)
    if (f[u][i] != f[v][i]) u = f[u][i], v = f[v][i];
  return f[u][0];
}
inline int input() {
  int t;
  scanf("%d", &t);
  return t;
}
int main() {
  n = input(), m = input();
  for (int i = 1; i <= m; ++i) {
    int u = input(), v = input(), w = input();
    add(u, v, w);
  }
  dfs(1, 0);
  for (int i = 1; i <= n; ++i) d[0][i] = dis[i];
  for (int j = 1; j <= 20; ++j)
    for (int i = 1; i <= n; ++i) f[i][j] = f[f[i][j - 1]][j - 1];
  sort(tmp + 1, tmp + tot + 1);
  int j = 1;
  for (int i = 2; i <= tot; ++i)
    if (tmp[j] != tmp[i]) tmp[++j] = tmp[i];
  for (int i = 1; i <= j; ++i) dijkstra(i, tmp[i]);
  for (int q = input(); q; q--) {
    int u = input(), v = input();
    long long ans = d[0][u] + d[0][v] - 2 * d[0][lca(u, v)];
    for (int i = 1; i <= j; ++i) ans = min(ans, d[i][u] + d[i][v]);
    printf("%lld\n", ans);
  }
  return 0;
}

```