#include <bits/stdc++.h>
#include <sys/time.h>
using namespace std;

#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

using ll = long long; using vll = vector<ll>; using vvll = vector<vll>; using P = pair<ll, ll>;
ll ugauss(ll a, ll b) { if (!a) return 0; if (a>0^b>0) return a/b; else return (a+(a>0?-1:1))/b+1; }
ll lgauss(ll a, ll b) { if (!a) return 0; if (a>0^b>0) return (a+(a>0?-1:1))/b-1; else return a/b; }
template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) {  o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args> 
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; o << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T> ostream &operator<<(ostream &o, const deque<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const unordered_set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U, typename V>  ostream &operator<<(ostream &o, const unordered_map<T, U, V> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]";  return o; }
vector<int> range(const int x, const int y) { vector<int> v(y - x + 1); iota(v.begin(), v.end(), x); return v; }
template <typename T> istream& operator>>(istream& i, vector<T>& o) { rep(j, o.size()) i >> o[j]; return i;}
template <typename T, typename S, typename U> ostream &operator<<(ostream &o, const priority_queue<T, S, U> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} return o; }
template <typename T> ostream &operator<<(ostream &o, const queue<T> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.front(); tmp.pop(); o << x << " ";} return o; }
template <typename T> ostream &operator<<(ostream &o, const stack<T> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} return o; }
template <typename T> unordered_map<T, ll> counter(vector<T> vec){unordered_map<T, ll> ret; for (auto&& x : vec) ret[x]++; return ret;};
void vizGraph(vvll& g, int mode = 0, string filename = "out.png") { ofstream ofs("./out.dot"); ofs << "digraph graph_name {" << endl; set<P> memo; rep(i, g.size())  rep(j, g[i].size()) { if (mode && (memo.count(P(i, g[i][j])) || memo.count(P(g[i][j], i)))) continue; memo.insert(P(i, g[i][j])); ofs << "    " << i << " -> " << g[i][j] << (mode ? " [arrowhead = none]" : "")<< endl;  } ofs << "}" << endl; ofs.close(); system(((string)"dot -T png out.dot >" + filename).c_str()); }
struct timeval start; double sec() { struct timeval tv; gettimeofday(&tv, NULL); return (tv.tv_sec - start.tv_sec) + (tv.tv_usec - start.tv_usec) * 1e-6; }
size_t random_seed; struct init_{init_(){ ios::sync_with_stdio(false); cin.tie(0); gettimeofday(&start, NULL); struct timeval myTime; struct tm *time_st; gettimeofday(&myTime, NULL); time_st = localtime(&myTime.tv_sec); srand(myTime.tv_usec); random_seed = RAND_MAX / 2 + rand() / 2; }} init__;
#define ldout fixed << setprecision(40) 

#define EPS (double)1e-14
#define INF (ll)1e18
#define mo  (ll)(1e9+7)

struct UnionFind {
    vector<int> data;
    UnionFind(int size) : data(size, -1) { }
    // x, yをマージ, O(A^-1)
    bool unite(int x, int y) {
        x = root(x); y = root(y);
        if (x != y) {
            if (data[y] < data[x]) swap(x, y);
            data[x] += data[y]; data[y] = x;
        }
        return x != y;
    }
    // x, yが同じ集合なら1, O(A^-1)
    bool find(int x, int y) {
        return root(x) == root(y);
    }
    // xの根を探す。同じ集合なら同じ根が帰る, O(A^-1)
    int root(int x) {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    // xが含まれる集合の大きさを返す, O(A^-1)
    int size(int x) {
        return -data[root(x)];
    }
    // 分離されている集合の数を返す, O(n)
    int getSetNum(void) {
        unordered_map<int, int> c;
        rep(i, data.size()) {
            c[root(i)]++;
        }
        return c.size();
    }
    // 頂点vと連結な集合を返す, O(n)
    vector<int> getContainingSet(int v) {
        vector<int> ret;
        for (int i = 0; i < data.size(); i++) 
            if (root(i) == root(v))
                ret.push_back(i);
        return ret;
    }

    // 集合ごとに全部の要素を出力, O(n)
    vector<vector<int>> getUnionList(void) {
        map<int, vector<int>> c;
        for (int i = 0; i < data.size(); i++) 
            c[root(i)].pb(i);
        vector<vector<int>> v;
        for (auto x : c) 
            v.push_back(x.second);
        return v;
    }
};
ostream &operator<<(ostream &o, struct UnionFind v) {  v.getUnionList(); int i = 0; for (auto x : v.getUnionList()) { o << i << "\t"; for (auto y : x) o << y << " "; o << endl; i++;} return o; }


ll n, m;
ll cost[4010][4010];
vector<vector<P>> g;
vector<vector<P>> t;
void update(ll i) {
    vector<bool> used(n);
    function<void(ll, ll, ll)> dfs = [&](ll i, ll j, ll c) {
        if (used[j]) return;
        used[j] = 1;
        cost[i][j] = c;
//        cout << mt(i, j) << " " << c << endl;
        for (auto uc : t[j]) {
            ll next_u = uc.fi;
            ll next_c = uc.se;
            dfs(i, next_u, max(cost[i][j], next_c));
        }
    };
    dfs(i, i, 0);
}
int main(void) {
    cin >> n >> m;
    g.resize(n);
    t.resize(n);

    vector<vll> edges;
    rep(i, m) {
        ll u, v, c; cin >> u >> v >> c; u--, v--;
        g[u].pb(P(v, c));
        g[v].pb(P(u, c));
        edges.pb((vll){c, u, v});
    }
    sort(all(edges));

    ll mst = 0;
    UnionFind uf(n);
    for (auto cuv : edges) {
        ll c = cuv[0];
        ll u = cuv[1];
        ll v = cuv[2];
        if (!uf.find(u, v)) {
            uf.unite(u, v);
            t[u].pb(P(v, c));
            t[v].pb(P(u, c));
            mst += c;
        }
    }
    /*
    cout << "##############" << endl;
    cout << mst << endl;
    cout << edges << endl;
    cout << t << endl;
    cout << uf << endl;
    */


    rep(i, n) rep(j, n) cost[i][j] = INF;
    rep(i, n) {
        update(i);
    }

    /*
    rep(i, n) {
        rep(j, n) {
            cout << cost[i][j] << " ";
        }
        cout << endl;
    }
    */

    ll q; cin >> q;
    rep(_, q) {
        ll x, y; cin >> x >> y; x--, y--;
        cout << mst - cost[x][y] << endl;
    }


    return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

Takahashi found an undirected connected graph with N vertices and M edges. The vertices are numbered 1 through N. The i-th edge connects vertices a_i and b_i, and has a weight of c_i.

He will play Q rounds of a game using this graph. In the i-th round, two vertices S_i and T_i are specified, and he will choose a subset of the edges such that any vertex can be reached from at least one of the vertices S_i or T_i by traversing chosen edges.

For each round, find the minimum possible total weight of the edges chosen by Takahashi.

Constraints

* 1 ≦ N ≦ 4,000
* 1 ≦ M ≦ 400,000
* 1 ≦ Q ≦ 100,000
* 1 ≦ a_i,b_i,S_i,T_i ≦ N
* 1 ≦ c_i ≦ 10^{9}
* a_i \neq b_i
* S_i \neq T_i
* The given graph is connected.

Input

The input is given from Standard Input in the following format:


N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M
Q
S_1 T_1
S_2 T_2
:
S_Q T_Q


Output

Print Q lines. The i-th line should contain the minimum possible total weight of the edges chosen by Takahashi.

Examples

Input

4 3
1 2 3
2 3 4
3 4 5
2
2 3
1 4


Output

8
7


Input

4 6
1 3 5
4 1 10
2 4 6
3 2 2
3 4 5
2 1 3
1
2 3


Output

8

### Response

```cpp
#include <bits/stdc++.h>
#include <sys/time.h>
using namespace std;

#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

using ll = long long; using vll = vector<ll>; using vvll = vector<vll>; using P = pair<ll, ll>;
ll ugauss(ll a, ll b) { if (!a) return 0; if (a>0^b>0) return a/b; else return (a+(a>0?-1:1))/b+1; }
ll lgauss(ll a, ll b) { if (!a) return 0; if (a>0^b>0) return (a+(a>0?-1:1))/b-1; else return a/b; }
template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) {  o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args> 
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; o << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T> ostream &operator<<(ostream &o, const deque<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const unordered_set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U, typename V>  ostream &operator<<(ostream &o, const unordered_map<T, U, V> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]";  return o; }
vector<int> range(const int x, const int y) { vector<int> v(y - x + 1); iota(v.begin(), v.end(), x); return v; }
template <typename T> istream& operator>>(istream& i, vector<T>& o) { rep(j, o.size()) i >> o[j]; return i;}
template <typename T, typename S, typename U> ostream &operator<<(ostream &o, const priority_queue<T, S, U> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} return o; }
template <typename T> ostream &operator<<(ostream &o, const queue<T> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.front(); tmp.pop(); o << x << " ";} return o; }
template <typename T> ostream &operator<<(ostream &o, const stack<T> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} return o; }
template <typename T> unordered_map<T, ll> counter(vector<T> vec){unordered_map<T, ll> ret; for (auto&& x : vec) ret[x]++; return ret;};
void vizGraph(vvll& g, int mode = 0, string filename = "out.png") { ofstream ofs("./out.dot"); ofs << "digraph graph_name {" << endl; set<P> memo; rep(i, g.size())  rep(j, g[i].size()) { if (mode && (memo.count(P(i, g[i][j])) || memo.count(P(g[i][j], i)))) continue; memo.insert(P(i, g[i][j])); ofs << "    " << i << " -> " << g[i][j] << (mode ? " [arrowhead = none]" : "")<< endl;  } ofs << "}" << endl; ofs.close(); system(((string)"dot -T png out.dot >" + filename).c_str()); }
struct timeval start; double sec() { struct timeval tv; gettimeofday(&tv, NULL); return (tv.tv_sec - start.tv_sec) + (tv.tv_usec - start.tv_usec) * 1e-6; }
size_t random_seed; struct init_{init_(){ ios::sync_with_stdio(false); cin.tie(0); gettimeofday(&start, NULL); struct timeval myTime; struct tm *time_st; gettimeofday(&myTime, NULL); time_st = localtime(&myTime.tv_sec); srand(myTime.tv_usec); random_seed = RAND_MAX / 2 + rand() / 2; }} init__;
#define ldout fixed << setprecision(40) 

#define EPS (double)1e-14
#define INF (ll)1e18
#define mo  (ll)(1e9+7)

struct UnionFind {
    vector<int> data;
    UnionFind(int size) : data(size, -1) { }
    // x, yをマージ, O(A^-1)
    bool unite(int x, int y) {
        x = root(x); y = root(y);
        if (x != y) {
            if (data[y] < data[x]) swap(x, y);
            data[x] += data[y]; data[y] = x;
        }
        return x != y;
    }
    // x, yが同じ集合なら1, O(A^-1)
    bool find(int x, int y) {
        return root(x) == root(y);
    }
    // xの根を探す。同じ集合なら同じ根が帰る, O(A^-1)
    int root(int x) {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    // xが含まれる集合の大きさを返す, O(A^-1)
    int size(int x) {
        return -data[root(x)];
    }
    // 分離されている集合の数を返す, O(n)
    int getSetNum(void) {
        unordered_map<int, int> c;
        rep(i, data.size()) {
            c[root(i)]++;
        }
        return c.size();
    }
    // 頂点vと連結な集合を返す, O(n)
    vector<int> getContainingSet(int v) {
        vector<int> ret;
        for (int i = 0; i < data.size(); i++) 
            if (root(i) == root(v))
                ret.push_back(i);
        return ret;
    }

    // 集合ごとに全部の要素を出力, O(n)
    vector<vector<int>> getUnionList(void) {
        map<int, vector<int>> c;
        for (int i = 0; i < data.size(); i++) 
            c[root(i)].pb(i);
        vector<vector<int>> v;
        for (auto x : c) 
            v.push_back(x.second);
        return v;
    }
};
ostream &operator<<(ostream &o, struct UnionFind v) {  v.getUnionList(); int i = 0; for (auto x : v.getUnionList()) { o << i << "\t"; for (auto y : x) o << y << " "; o << endl; i++;} return o; }


ll n, m;
ll cost[4010][4010];
vector<vector<P>> g;
vector<vector<P>> t;
void update(ll i) {
    vector<bool> used(n);
    function<void(ll, ll, ll)> dfs = [&](ll i, ll j, ll c) {
        if (used[j]) return;
        used[j] = 1;
        cost[i][j] = c;
//        cout << mt(i, j) << " " << c << endl;
        for (auto uc : t[j]) {
            ll next_u = uc.fi;
            ll next_c = uc.se;
            dfs(i, next_u, max(cost[i][j], next_c));
        }
    };
    dfs(i, i, 0);
}
int main(void) {
    cin >> n >> m;
    g.resize(n);
    t.resize(n);

    vector<vll> edges;
    rep(i, m) {
        ll u, v, c; cin >> u >> v >> c; u--, v--;
        g[u].pb(P(v, c));
        g[v].pb(P(u, c));
        edges.pb((vll){c, u, v});
    }
    sort(all(edges));

    ll mst = 0;
    UnionFind uf(n);
    for (auto cuv : edges) {
        ll c = cuv[0];
        ll u = cuv[1];
        ll v = cuv[2];
        if (!uf.find(u, v)) {
            uf.unite(u, v);
            t[u].pb(P(v, c));
            t[v].pb(P(u, c));
            mst += c;
        }
    }
    /*
    cout << "##############" << endl;
    cout << mst << endl;
    cout << edges << endl;
    cout << t << endl;
    cout << uf << endl;
    */


    rep(i, n) rep(j, n) cost[i][j] = INF;
    rep(i, n) {
        update(i);
    }

    /*
    rep(i, n) {
        rep(j, n) {
            cout << cost[i][j] << " ";
        }
        cout << endl;
    }
    */

    ll q; cin >> q;
    rep(_, q) {
        ll x, y; cin >> x >> y; x--, y--;
        cout << mst - cost[x][y] << endl;
    }


    return 0;
}

```