#include <bits/stdc++.h>
using namespace std;
const int maxn = 200055;
const int logn = 55;
const long long int inff = 1e18;
priority_queue<pair<long long int, int>, vector<pair<long long int, int> >,
               greater<pair<long long int, int> > >
    q;
int n, m, st[maxn], nex[maxn], to[maxn];
int fa[maxn], v[maxn], deep[maxn];
int note[maxn], to1[maxn];
long long int dist[logn][maxn], dis1[maxn], dis[maxn], ll[maxn];
int jfa[maxn][logn];
int tm;
void dij(int x) {
  int i, rt = note[x], y;
  for (i = 1; i <= n; i++) {
    dist[rt][i] = inff;
  }
  for (i = 1; i <= n; i++) {
    v[i] = 0;
  }
  q.push(make_pair(0, x));
  dist[rt][x] = 0;
  while (!q.empty()) {
    while (!q.empty() && v[q.top().second] != 0) q.pop();
    if (q.empty()) break;
    y = q.top().second;
    v[y] = 1;
    q.pop();
    for (i = st[y]; i != 0; i = nex[i]) {
      if (v[to[i]]) continue;
      if (dist[rt][y] + dis[i] < dist[rt][to[i]]) {
        dist[rt][to[i]] = dist[rt][y] + dis[i];
        q.push(make_pair(dist[rt][to[i]], to[i]));
      }
    }
  }
  return;
}
void adde(int s, int t, long long int d) {
  tm++;
  to[tm] = t;
  dis[tm] = d;
  nex[tm] = st[s];
  st[s] = tm;
  return;
}
int lca(int ta, int tb) {
  int i, a, b;
  a = ta;
  b = tb;
  if (deep[a] < deep[b]) swap(a, b);
  for (i = 20; i >= 0; i--) {
    if (deep[jfa[a][i]] >= deep[b]) a = jfa[a][i];
  }
  if (a == b) return a;
  for (i = 20; i >= 0; i--) {
    if (jfa[a][i] != 0 && jfa[b][i] != 0 && jfa[a][i] != jfa[b][i]) {
      a = jfa[a][i];
      b = jfa[b][i];
    }
  }
  return fa[a];
}
void dfs(int x) {
  int i;
  v[x] = 1;
  for (i = st[x]; i != 0; i = nex[i]) {
    if (v[to[i]] == 1) continue;
    fa[to[i]] = x;
    deep[to[i]] = deep[x] + 1;
    ll[to[i]] = ll[x] + dis[i];
    dis1[to[i]] = dis[i];
    dfs(to[i]);
  }
  return;
}
long long int disss(int x, int y) { return ll[x] + ll[y] - ll[lca(x, y)] * 2; }
int main() {
  int i, j, s, t;
  long long int d;
  scanf("%d%d", &n, &m);
  for (i = 1; i <= m; i++) {
    scanf("%d%d%lld", &s, &t, &d);
    adde(s, t, d);
    adde(t, s, d);
  }
  deep[1] = 1;
  ll[1] = 0;
  dfs(1);
  for (i = 1; i <= n; i++) {
    jfa[i][0] = fa[i];
  }
  for (j = 1; j <= 20; j++) {
    for (i = 1; i <= n; i++) jfa[i][j] = jfa[jfa[i][j - 1]][j - 1];
  }
  dij(1);
  tm = 0;
  for (j = 1; j <= n; j++) {
    for (i = st[j]; i != 0; i = nex[i]) {
      if (fa[to[i]] != j && fa[j] != to[i]) {
        tm++;
        note[j] = tm;
        to1[tm] = j;
        dij(j);
        i = 0;
      }
    }
  }
  int q;
  long long int ans;
  scanf("%d", &q);
  for (j = 1; j <= q; j++) {
    scanf("%d%d", &s, &t);
    ans = disss(s, t);
    for (i = 1; i <= tm; i++) {
      ans = min(ans, dist[i][s] + dist[i][t]);
    }
    printf("%lld\n", ans);
  }
  return 0;
}

### Prompt

Create a solution in cpp for 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 maxn = 200055;
const int logn = 55;
const long long int inff = 1e18;
priority_queue<pair<long long int, int>, vector<pair<long long int, int> >,
               greater<pair<long long int, int> > >
    q;
int n, m, st[maxn], nex[maxn], to[maxn];
int fa[maxn], v[maxn], deep[maxn];
int note[maxn], to1[maxn];
long long int dist[logn][maxn], dis1[maxn], dis[maxn], ll[maxn];
int jfa[maxn][logn];
int tm;
void dij(int x) {
  int i, rt = note[x], y;
  for (i = 1; i <= n; i++) {
    dist[rt][i] = inff;
  }
  for (i = 1; i <= n; i++) {
    v[i] = 0;
  }
  q.push(make_pair(0, x));
  dist[rt][x] = 0;
  while (!q.empty()) {
    while (!q.empty() && v[q.top().second] != 0) q.pop();
    if (q.empty()) break;
    y = q.top().second;
    v[y] = 1;
    q.pop();
    for (i = st[y]; i != 0; i = nex[i]) {
      if (v[to[i]]) continue;
      if (dist[rt][y] + dis[i] < dist[rt][to[i]]) {
        dist[rt][to[i]] = dist[rt][y] + dis[i];
        q.push(make_pair(dist[rt][to[i]], to[i]));
      }
    }
  }
  return;
}
void adde(int s, int t, long long int d) {
  tm++;
  to[tm] = t;
  dis[tm] = d;
  nex[tm] = st[s];
  st[s] = tm;
  return;
}
int lca(int ta, int tb) {
  int i, a, b;
  a = ta;
  b = tb;
  if (deep[a] < deep[b]) swap(a, b);
  for (i = 20; i >= 0; i--) {
    if (deep[jfa[a][i]] >= deep[b]) a = jfa[a][i];
  }
  if (a == b) return a;
  for (i = 20; i >= 0; i--) {
    if (jfa[a][i] != 0 && jfa[b][i] != 0 && jfa[a][i] != jfa[b][i]) {
      a = jfa[a][i];
      b = jfa[b][i];
    }
  }
  return fa[a];
}
void dfs(int x) {
  int i;
  v[x] = 1;
  for (i = st[x]; i != 0; i = nex[i]) {
    if (v[to[i]] == 1) continue;
    fa[to[i]] = x;
    deep[to[i]] = deep[x] + 1;
    ll[to[i]] = ll[x] + dis[i];
    dis1[to[i]] = dis[i];
    dfs(to[i]);
  }
  return;
}
long long int disss(int x, int y) { return ll[x] + ll[y] - ll[lca(x, y)] * 2; }
int main() {
  int i, j, s, t;
  long long int d;
  scanf("%d%d", &n, &m);
  for (i = 1; i <= m; i++) {
    scanf("%d%d%lld", &s, &t, &d);
    adde(s, t, d);
    adde(t, s, d);
  }
  deep[1] = 1;
  ll[1] = 0;
  dfs(1);
  for (i = 1; i <= n; i++) {
    jfa[i][0] = fa[i];
  }
  for (j = 1; j <= 20; j++) {
    for (i = 1; i <= n; i++) jfa[i][j] = jfa[jfa[i][j - 1]][j - 1];
  }
  dij(1);
  tm = 0;
  for (j = 1; j <= n; j++) {
    for (i = st[j]; i != 0; i = nex[i]) {
      if (fa[to[i]] != j && fa[j] != to[i]) {
        tm++;
        note[j] = tm;
        to1[tm] = j;
        dij(j);
        i = 0;
      }
    }
  }
  int q;
  long long int ans;
  scanf("%d", &q);
  for (j = 1; j <= q; j++) {
    scanf("%d%d", &s, &t);
    ans = disss(s, t);
    for (i = 1; i <= tm; i++) {
      ans = min(ans, dist[i][s] + dist[i][t]);
    }
    printf("%lld\n", ans);
  }
  return 0;
}

```