#pragma GCC optimize ("Ofast")
#include<bits/stdc++.h>
using namespace std;
void *wmem;
char memarr[96000000];
template<class S, class T> inline S min_L(S a,T b){
  return a<=b?a:b;
}
template<class S, class T> inline S max_L(S a,T b){
  return a>=b?a:b;
}
template<class T> inline void walloc1d(T **arr, int x, void **mem = &wmem){
  static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
  (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] );
  (*arr)=(T*)(*mem);
  (*mem)=((*arr)+x);
}
inline int my_getchar_unlocked(){
  static char buf[1048576];
  static int s = 1048576;
  static int e = 1048576;
  if(s == e && e == 1048576){
    e = fread_unlocked(buf, 1, 1048576, stdin);
    s = 0;
  }
  if(s == e){
    return EOF;
  }
  return buf[s++];
}
inline void rd(int &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline void rd(long long &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline int rd_int(void){
  int x;
  rd(x);
  return x;
}
struct MY_WRITER{
  char buf[1048576];
  int s;
  int e;
  MY_WRITER(){
    s = 0;
    e = 1048576;
  }
  ~MY_WRITER(){
    if(s){
      fwrite_unlocked(buf, 1, s, stdout);
    }
  }
}
;
MY_WRITER MY_WRITER_VAR;
void my_putchar_unlocked(int a){
  if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){
    fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout);
    MY_WRITER_VAR.s = 0;
  }
  MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a;
}
inline void wt_L(char a){
  my_putchar_unlocked(a);
}
inline void wt_L(int x){
  int s=0;
  int m=0;
  char f[10];
  if(x<0){
    m=1;
    x=-x;
  }
  while(x){
    f[s++]=x%10;
    x/=10;
  }
  if(!s){
    f[s++]=0;
  }
  if(m){
    my_putchar_unlocked('-');
  }
  while(s--){
    my_putchar_unlocked(f[s]+'0');
  }
}
inline void wt_L(long long x){
  int s=0;
  int m=0;
  char f[20];
  if(x<0){
    m=1;
    x=-x;
  }
  while(x){
    f[s++]=x%10;
    x/=10;
  }
  if(!s){
    f[s++]=0;
  }
  if(m){
    my_putchar_unlocked('-');
  }
  while(s--){
    my_putchar_unlocked(f[s]+'0');
  }
}
template<class S, class T> inline S chmin(S &a, T b){
  if(a>b){
    a=b;
  }
  return a;
}
template <class T> struct DijkstraHeap{
  int *hp;
  int *place;
  int size;
  char *visited;
  T *val;
  void malloc(int N){
    hp = (int*)std::malloc(N*sizeof(int));
    place = (int*)std::malloc(N*sizeof(int));
    visited = (char*)std::malloc(N*sizeof(char));
    val = (T*)std::malloc(N*sizeof(T));
  }
  void free(){
    std::free(hp);
    std::free(place);
    std::free(visited);
    std::free(val);
  }
  void walloc(int N, void **mem=&wmem){
    walloc1d(&hp, N, mem);
    walloc1d(&place, N, mem);
    walloc1d(&visited, N, mem);
    walloc1d(&val, N, mem);
  }
  void init(int N){
    int i;
    size = 0;
    for(i=(0);i<(N);i++){
      place[i]=-1;
    }
    for(i=(0);i<(N);i++){
      visited[i]=0;
    }
  }
  void up(int n){
    int m;
    while(n){
      m=(n-1)/2;
      if(val[hp[m]]<=val[hp[n]]){
        break;
      }
      swap(hp[m],hp[n]);
      swap(place[hp[m]],place[hp[n]]);
      n=m;
    }
  }
  void down(int n){
    int m;
    for(;;){
      m=2*n+1;
      if(m>=size){
        break;
      }
      if(m+1<size&&val[hp[m]]>val[hp[m+1]]){
        m++;
      }
      if(val[hp[m]]>=val[hp[n]]){
        break;
      }
      swap(hp[m],hp[n]);
      swap(place[hp[m]],place[hp[n]]);
      n=m;
    }
  }
  void change(int n, T v){
    if(visited[n]||(place[n]>=0&&val[n]<=v)){
      return;
    }
    val[n]=v;
    if(place[n]==-1){
      place[n]=size;
      hp[size++]=n;
      up(place[n]);
    }
    else{
      up(place[n]);
    }
  }
  int pop(void){
    int res=hp[0];
    place[res]=-1;
    size--;
    if(size){
      hp[0]=hp[size];
      place[hp[0]]=0;
      down(0);
    }
    visited[res]=1;
    return res;
  }
}
;
template<class T> struct segtree{
  int N;
  int logN;
  T *sum;
  T *mn;
  int *mnind;
  T *fixval;
  char *fixed;
  T *addval;
  void malloc(int maxN, int once = 0){
    int i;
    for(i=1;i<maxN;i*=2){
      ;
    }
    sum = new T[2*i];
    mn = new T[2*i];
    mnind = new int[2*i];
    fixval = new T[i];
    addval = new T[i];
    fixed = new char[i];
    if(once){
      setN(maxN);
    }
  }
  void walloc(int maxN, int once = 0, void **mem = &wmem){
    int i;
    for(i=1;i<maxN;i*=2){
      ;
    }
    walloc1d(&sum, 2*i, mem);
    walloc1d(&mn, 2*i, mem);
    walloc1d(&mnind, 2*i, mem);
    walloc1d(&fixval, i, mem);
    walloc1d(&addval, i, mem);
    walloc1d(&fixed, i, mem);
    if(once){
      setN(maxN);
    }
  }
  void free(void){
    delete [] sum;
    delete [] mn;
    delete [] mnind;
    delete [] fixval;
    delete [] addval;
    delete [] fixed;
  }
  T& operator[](int i){
    return sum[N+i];
  }
  void setN(int n, int zerofill = 1, int dobuild = 1){
    int i;
    for(i=1,logN=0;i<n;i*=2,logN++){
      ;
    }
    N = i;
    if(zerofill){
      for(i=(0);i<(N);i++){
        sum[N+i] = 0;
      }
    }
    if(dobuild){
      build();
    }
  }
  void build(void){
    int i;
    for(i=(0);i<(N);i++){
      mn[N+i] = sum[N+i];
      mnind[N+i] = i;
    }
    for(i=N-1;i;i--){
      sum[i] = sum[2*i] + sum[2*i+1];
      if(mn[2*i] <= mn[2*i+1]){
        mn[i] = mn[2*i];
        mnind[i] = mnind[2*i];
      }
      else{
        mn[i] = mn[2*i+1];
        mnind[i] = mnind[2*i+1];
      }
    }
    int Wu3kZ3t7 = N;
    for(i=(1);i<(Wu3kZ3t7);i++){
      fixed[i] = 0;
    }
    int grBCmONb = N;
    for(i=(1);i<(grBCmONb);i++){
      addval[i] = 0;
    }
  }
  inline void push_one(int a, int sz, int st){
    if(fixed[a]){
      if(sz > 1){
        fixed[a*2] = fixed[a*2+1] = 1;
        fixval[a*2] = fixval[a*2+1] = fixval[a];
        sum[a*2] = sum[a*2+1] = sz * fixval[a];
        mn[a*2] = mn[a*2+1] = fixval[a];
        mnind[a*2] = st;
        mnind[a*2+1] = st + sz;
      }
      else{
        sum[a*2] = sum[a*2+1] = sz * fixval[a];
        mn[a*2] = mn[a*2+1] = fixval[a];
        mnind[a*2] = st;
        mnind[a*2+1] = st + sz;
      }
      fixed[a] = 0;
      addval[a] = 0;
      return;
    }
    if(addval[a] != 0){
      if(sz > 1){
        if(fixed[a*2]){
          fixval[a*2] += addval[a];
        }
        else{
          addval[a*2] += addval[a];
        }
        if(fixed[a*2+1]){
          fixval[a*2+1] += addval[a];
        }
        else{
          addval[a*2+1] += addval[a];
        }
        sum[a*2] += sz * addval[a];
        sum[a*2+1] += sz * addval[a];
        mn[a*2] += addval[a];
        mn[a*2+1] += addval[a];
      }
      else{
        sum[a*2] += sz * addval[a];
        sum[a*2+1] += sz * addval[a];
        mn[a*2] += addval[a];
        mn[a*2+1] += addval[a];
      }
      addval[a] = 0;
      return;
    }
  }
  inline void push(int a){
    int i;
    int aa = a - N;
    int nd;
    int sz;
    int st;
    for(i=logN;i;i--){
      nd = a>>i;
      sz = 1<<(i-1);
      st = 2 * sz * (aa>>i);
      push_one(nd, sz, st);
    }
  }
  inline void build(int a){
    int sz = 1;
    int st = a - N;
    while(a > 1){
      if(a%2){
        st += sz;
      }
      a /= 2;
      sz *= 2;
      if(fixed[a]){
        sum[a] = sz * fixval[a];
        mn[a] = fixval[a];
      }
      else{
        sum[a] = sum[a*2] + sum[a*2+1];
        if(mn[a*2] <= mn[a*2+1]){
          mn[a] = mn[a*2];
          mnind[a] = mnind[a*2];
        }
        else{
          mn[a] = mn[a*2+1];
          mnind[a] = mnind[a*2+1];
        }
        if(addval[a] != 0){
          mn[a] += addval[a];
          sum[a] += sz * addval[a];
        }
      }
    }
  }
  inline void change(int a, int b, T val){
    int sz = 1;
    int aa;
    int bb;
    int st_a = a;
    int st_b = b;
    if(a >= b){
      return;
    }
    aa = (a += N);
    bb = (b += N);
    push(a);
    push(b-1);
    if(a%2){
      sum[a] = mn[a] = val;
      a++;
      st_a += sz;
    }
    if(b%2){
      b--;
      st_b -= sz;
      sum[b] = mn[b] = val;
    }
    a /= 2;
    b /= 2;
    while(a < b){
      sz *= 2;
      if(a%2){
        fixed[a]=1;
        fixval[a]=val;
        sum[a] = sz * val;
        mn[a] = val;
        mnind[a] = st_a;
        a++;
        st_a += sz;
      }
      if(b%2){
        b--;
        st_b -= sz;
        fixed[b]=1;
        fixval[b]=val;
        sum[b] = sz * val;
        mn[b] = val;
        mnind[b] = st_b;
      }
      a /= 2;
      b /= 2;
    }
    build(aa);
    build(bb-1);
  }
  inline void add(int a, int b, T val){
    int sz = 1;
    int aa;
    int bb;
    if(a >= b){
      return;
    }
    aa = (a += N);
    bb = (b += N);
    push(a);
    push(b-1);
    if(a%2){
      sum[a] += val;
      mn[a] += val;
      a++;
    }
    if(b%2){
      b--;
      sum[b] += val;
      mn[b] += val;
    }
    a /= 2;
    b /= 2;
    while(a < b){
      sz *= 2;
      if(a%2){
        if(fixed[a]){
          fixval[a] += val;
        }
        else{
          addval[a] += val;
        }
        sum[a] += sz * val;
        mn[a] += val;
        a++;
      }
      if(b%2){
        b--;
        if(fixed[b]){
          fixval[b] += val;
        }
        else{
          addval[b] += val;
        }
        sum[b] += sz * val;
        mn[b] += val;
      }
      a /= 2;
      b /= 2;
    }
    build(aa);
    build(bb-1);
  }
  inline pair<T,int> getMin(int a, int b){
    pair<T,int> res;
    pair<T,int> tmp;
    int fga = 0;
    int fgb = 0;
    a += N;
    b += N;
    push(a);
    push(b-1);
    while(a < b){
      if(a%2){
        if(fga){
          res =min_L(res, make_pair(mn[a], mnind[a]));
        }
        else{
          res = make_pair(mn[a], mnind[a]);
          fga = 1;
        }
        a++;
      }
      if(b%2){
        b--;
        if(fgb){
          tmp =min_L(make_pair(mn[b], mnind[b]), tmp);
        }
        else{
          tmp = make_pair(mn[b], mnind[b]);
          fgb = 1;
        }
      }
      a /= 2;
      b /= 2;
    }
    if(fga==1 && fgb==0){
      return res;
    }
    if(fga==0 && fgb==1){
      return tmp;
    }
    if(fga==1 && fgb==1){
      res =min_L(res, tmp);
      return res;
    }
    return res;
  }
  inline T getMinVal(int a, int b){
    T res;
    T tmp;
    int fga = 0;
    int fgb = 0;
    a += N;
    b += N;
    push(a);
    push(b-1);
    while(a < b){
      if(a%2){
        if(fga){
          res =min_L(res, mn[a]);
        }
        else{
          res = mn[a];
          fga = 1;
        }
        a++;
      }
      if(b%2){
        b--;
        if(fgb){
          tmp =min_L(mn[b], tmp);
        }
        else{
          tmp = mn[b];
          fgb = 1;
        }
      }
      a /= 2;
      b /= 2;
    }
    if(fga==1 && fgb==0){
      return res;
    }
    if(fga==0 && fgb==1){
      return tmp;
    }
    if(fga==1 && fgb==1){
      res =min_L(res, tmp);
      return res;
    }
    return res;
  }
  inline int getMinInd(int a, int b){
    return getMin(a,b).second;
  }
  inline T getSum(int a, int b){
    T res;
    T tmp;
    int fga = 0;
    int fgb = 0;
    a += N;
    b += N;
    push(a);
    push(b-1);
    while(a < b){
      if(a%2){
        if(fga){
          res = res + sum[a];
        }
        else{
          res = sum[a];
          fga = 1;
        }
        a++;
      }
      if(b%2){
        b--;
        if(fgb){
          tmp = sum[b] + tmp;
        }
        else{
          tmp = sum[b];
          fgb = 1;
        }
      }
      a /= 2;
      b /= 2;
    }
    if(fga==1 && fgb==0){
      return res;
    }
    if(fga==0 && fgb==1){
      return tmp;
    }
    if(fga==1 && fgb==1){
      res = res + tmp;
      return res;
    }
    return res;
  }
}
;
struct graph{
  int N;
  int *es;
  int **edge;
  void setEdge(int N__, int M, int A[], int B[], void **mem = &wmem){
    int i;
    N = N__;
    walloc1d(&es, N, mem);
    walloc1d(&edge, N, mem);
    for(i=(0);i<(N);i++){
      es[i] = 0;
    }
    for(i=(0);i<(M);i++){
      es[A[i]]++;
      es[B[i]]++;
    }
    for(i=(0);i<(N);i++){
      walloc1d(&edge[i], es[i], mem);
    }
    for(i=(0);i<(N);i++){
      es[i] = 0;
    }
    for(i=(0);i<(M);i++){
      edge[A[i]][es[A[i]]++] = B[i];
      edge[B[i]][es[B[i]]++] = A[i];
    }
  }
  void getDist(int root, int res[], void *mem = wmem){
    int i;
    int j;
    int k;
    int*q;
    int s;
    int z;
    walloc1d(&q, N, &mem);
    for(i=(0);i<(N);i++){
      res[i]=-1;
    }
    res[root]=0;
    s=0;
    z=1;
    q[0]=root;
    while(z){
      i=q[s++];
      z--;
      for(j=(0);j<(es[i]);j++){
        k=edge[i][j];
        if(res[k]>=0){
          continue;
        }
        res[k]=res[i]+1;
        q[s+z++]=k;
      }
    }
  }
}
;
template<class T> struct wgraph{
  int N;
  int *es;
  int **edge;
  T **cost;
  graph g;
  void setEdge(int N__, int M, int A[], int B[], T C[], void **mem = &wmem){
    int i;
    N = N__;
    walloc1d(&es, N, mem);
    for(i=(0);i<(N);i++){
      es[i] = 0;
    }
    for(i=(0);i<(M);i++){
      es[A[i]]++;
      es[B[i]]++;
    }
    walloc1d(&edge, N, mem);
    for(i=(0);i<(N);i++){
      walloc1d(&edge[i], es[i], mem);
    }
    walloc1d(&cost, N, mem);
    for(i=(0);i<(N);i++){
      walloc1d(&cost[i], es[i], mem);
    }
    for(i=(0);i<(N);i++){
      es[i] = 0;
    }
    for(i=(0);i<(M);i++){
      edge[A[i]][es[A[i]]] = B[i];
      edge[B[i]][es[B[i]]] = A[i];
      cost[A[i]][es[A[i]]++] = C[i];
      cost[B[i]][es[B[i]]++] = C[i];
    }
    g.N = N;
    g.es = es;
    g.edge = edge;
  }
  template<class S> void getDist(int root, S res[], S unreachable = -1, void *mem = wmem){
    int i;
    int j;
    DijkstraHeap<S> hp;
    hp.walloc(N, &mem);
    hp.init(N);
    hp.change(root,0);
    while(hp.size){
      i = hp.pop();
      for(j=(0);j<(es[i]);j++){
        hp.change(edge[i][j], hp.val[i]+cost[i][j]);
      }
    }
    for(i=(0);i<(N);i++){
      res[i] = (hp.visited[i] ? hp.val[i] : unreachable);
    }
  }
}
;
struct HLD{
  int N;
  int *es;
  int **edge;
  int *group;
  int *groupind;
  int groupNum;
  int *groupSize;
  int **groupNode;
  int *groupUpNode;
  int *groupDepth;
  void init(graph g, void **mem = &wmem){
    init(g.N, g.es, g.edge, mem);
  }
  void init(int N__, int *es__, int **edge__, void **mem = &wmem){
    int i;
    int j;
    int k;
    int x;
    int y;
    int mx;
    int *q;
    int q_st;
    int q_ed;
    int *sz;
    char *vis;
    void *tmpmem;
    N = N__;
    es = es__;
    edge = edge__;
    walloc1d(&group, N, mem);
    walloc1d(&groupind, N, mem);
    tmpmem = *mem;
    walloc1d(&q, N, &tmpmem);
    walloc1d(&sz, N, &tmpmem);
    walloc1d(&vis, N, &tmpmem);
    for(i=(0);i<(N);i++){
      vis[i] = 0;
    }
    q_st = 0;
    q_ed = 1;
    q[0] = 0;
    vis[0] = 1;
    while(q_st < q_ed){
      i = q[q_st++];
      for(j=(0);j<(es[i]);j++){
        k = edge[i][j];
        if(!vis[k]){
          vis[k] = 1;
          q[q_ed++] = k;
        }
      }
    }
    for(i=(0);i<(N);i++){
      sz[i] = 0;
    }
    for(j=N-1;j>=0;j--){
      i = q[j];
      sz[i] = 1;
      for(k=(0);k<(es[i]);k++){
        sz[i] += sz[edge[i][k]];
      }
    }
    for(i=(0);i<(N);i++){
      group[i] = -1;
    }
    groupNum = 0;
    for(j=(0);j<(N);j++){
      i = q[j];
      if(group[i]>=0){
        continue;
      }
      group[i] = groupNum++;
      groupind[i] = 0;
      for(;;){
        mx = -1;
        for(k=(0);k<(es[i]);k++){
          if(group[edge[i][k]] != -1){
            continue;
          }
          if(mx==-1){
            mx = k;
          }
          else if(sz[edge[i][k]] > sz[edge[i][mx]]){
            mx = k;
          }
        }
        if(mx==-1){
          break;
        }
        group[edge[i][mx]] = group[i];
        groupind[edge[i][mx]] = groupind[i]+1;
        i = edge[i][mx];
      }
    }
    walloc1d(&groupSize, groupNum, mem);
    walloc1d(&groupUpNode, groupNum, mem);
    walloc1d(&groupDepth, groupNum, mem);
    for(i=(0);i<(groupNum);i++){
      groupSize[i] = 0;
    }
    for(i=(0);i<(N);i++){
      groupSize[group[i]]++;
    }
    walloc1d(&groupNode, groupNum, mem);
    for(i=(0);i<(groupNum);i++){
      walloc1d(&groupNode[i], groupSize[i], mem);
    }
    for(i=(0);i<(N);i++){
      groupNode[group[i]][groupind[i]] = i;
    }
    for(i=(0);i<(groupNum);i++){
      groupDepth[i] = -1;
    }
    groupUpNode[0] = -1;
    groupDepth[0] = 0;
    for(x=(0);x<(groupNum);x++){
      for(y=(0);y<(groupSize[x]);y++){
        i = groupNode[x][y];
        for(j=(0);j<(es[i]);j++){
          k = edge[i][j];
          if(x != group[k] && groupDepth[group[k]]==-1){
            groupUpNode[group[k]] = i;
            groupDepth[group[k]] = groupDepth[x] + 1;
          }
        }
      }
    }
  }
  int lca(int x, int y){
    int x1;
    int y1;
    int x2;
    int y2;
    x1 = group[x];
    x2 = groupind[x];
    y1 = group[y];
    y2 = groupind[y];
    while(groupDepth[x1] > groupDepth[y1]){
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
    }
    while(groupDepth[x1] < groupDepth[y1]){
      y = groupUpNode[y1];
      y1 = group[y];
      y2 = groupind[y];
    }
    while(x1 != y1){
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
      y = groupUpNode[y1];
      y1 = group[y];
      y2 = groupind[y];
    }
    if(x2 <= y2){
      return x;
    }
    return y;
  }
  int depth(int x){
    int x1;
    int x2;
    int res = 0;
    x1 = group[x];
    x2 = groupind[x];
    while(groupUpNode[x1] != -1){
      res += x2 + 1;
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
    }
    return res + x2;
  }
  int dist(int x, int y){
    int x1;
    int y1;
    int x2;
    int y2;
    int res = 0;
    x1 = group[x];
    x2 = groupind[x];
    y1 = group[y];
    y2 = groupind[y];
    while(groupDepth[x1] > groupDepth[y1]){
      res += x2 + 1;
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
    }
    while(groupDepth[x1] < groupDepth[y1]){
      res += y2 + 1;
      y = groupUpNode[y1];
      y1 = group[y];
      y2 = groupind[y];
    }
    while(x1 != y1){
      res += x2 + y2 + 2;
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
      y = groupUpNode[y1];
      y1 = group[y];
      y2 = groupind[y];
    }
    if(x2 <= y2){
      return res + y2 - x2;
    }
    return res + x2 - y2;
  }
  int up(int x){
    int x1 = group[x];
    int x2 = groupind[x];
    if(x2==0){
      return groupUpNode[x1];
    }
    return groupNode[x1][x2-1];
  }
  int up(int x, int d){
    int x1 = group[x];
    int x2 = groupind[x];
    while(d > x2){
      if(groupUpNode[x1]==-1){
        return -1;
      }
      d -= x2 + 1;
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
    }
    return groupNode[x1][x2-d];
  }
}
;
template<class T> struct HLD_segtree{
  HLD *hld;
  segtree<T> *seg;
  void init(HLD *hld__, T initval[], void **mem = &wmem){
    int i;
    int j;
    hld = hld__;
    walloc1d(&seg, hld->groupNum, mem);
    for(i=(0);i<(hld->groupNum);i++){
      seg[i].walloc(hld->groupSize[i], 0, mem);
      seg[i].setN(hld->groupSize[i], 0, 0);
      if(initval!=NULL){
        for(j=(0);j<(hld->groupSize[i]);j++){
          seg[i][j] = initval[ hld->groupNode[i][j] ];
        }
      }
      else{
        for(j=(0);j<(hld->groupSize[i]);j++){
          seg[i][j] = 0;
        }
      }
      seg[i].build();
    }
  }
  inline void change(int u, int v, T val){
    int ug;
    int vg;
    int ui;
    int vi;
    ug = hld->group[u];
    vg = hld->group[v];
    while(ug != vg){
      if(hld->groupDepth[ug] < hld->groupDepth[vg]){
        swap(u, v);
        swap(ug, vg);
      }
      seg[ug].change(0, hld->groupind[u]+1, val);
      u = hld->groupUpNode[ug];
      ug = hld->group[u];
    }
    ui = hld->groupind[u];
    vi = hld->groupind[v];
    seg[ug].change(min_L(ui, vi),max_L(ui, vi)+1, val);
  }
  inline void add(int u, int v, T val){
    int ug;
    int vg;
    int ui;
    int vi;
    ug = hld->group[u];
    vg = hld->group[v];
    while(ug != vg){
      if(hld->groupDepth[ug] < hld->groupDepth[vg]){
        swap(u, v);
        swap(ug, vg);
      }
      seg[ug].add(0, hld->groupind[u]+1, val);
      u = hld->groupUpNode[ug];
      ug = hld->group[u];
    }
    ui = hld->groupind[u];
    vi = hld->groupind[v];
    seg[ug].add(min_L(ui, vi),max_L(ui, vi)+1, val);
  }
  inline pair<T,int> getMin(int u, int v){
    pair<T,int> res;
    pair<T,int> tmp;
    int ug;
    int vg;
    int ui;
    int vi;
    ug = hld->group[u];
    vg = hld->group[v];
    res.first = numeric_limits<T>::max();
    res.second = -1;
    while(ug != vg){
      if(hld->groupDepth[ug] < hld->groupDepth[vg]){
        swap(u, v);
        swap(ug, vg);
      }
      tmp = seg[ug].getMin(0, hld->groupind[u]+1);
      tmp.second = hld->groupNode[ug][tmp.second];
      chmin(res, tmp);
      u = hld->groupUpNode[ug];
      ug = hld->group[u];
    }
    ui = hld->groupind[u];
    vi = hld->groupind[v];
    tmp = seg[ug].getMin(min_L(ui, vi),max_L(ui, vi)+1);
    tmp.second = hld->groupNode[ug][tmp.second];
    chmin(res, tmp);
    return res;
  }
  inline T getMinVal(int u, int v){
    return getMin(u,v).first;
  }
  inline int getMinInd(int u, int v){
    return getMin(u,v).second;
  }
  inline T getSum(int u, int v){
    T res;
    int ug;
    int vg;
    int ui;
    int vi;
    ug = hld->group[u];
    vg = hld->group[v];
    res = 0;
    while(ug != vg){
      if(hld->groupDepth[ug] < hld->groupDepth[vg]){
        swap(u, v);
        swap(ug, vg);
      }
      res += seg[ug].getSum(0, hld->groupind[u]+1);
      u = hld->groupUpNode[ug];
      ug = hld->group[u];
    }
    ui = hld->groupind[u];
    vi = hld->groupind[v];
    res += seg[ug].getSum(min_L(ui, vi),max_L(ui, vi)+1);
    return res;
  }
}
;
int N;
int A[100000];
int B[100000];
long long C[100000];
int X;
int Y;
wgraph<long long> g;
HLD hld;
HLD_segtree<long long> t;
HLD_segtree<long long> tdis;
int dep[100000];
long long mn1[100000];
long long mn2[100000];
long long mn3[100000];
long long mn[100000];
long long updis[100000];
long long cand[3];
int main(){
  int a2conNHc, i;
  wmem = memarr;
  int xx;
  int yy;
  int xxx;
  int yyy;
  int z;
  long long res;
  long long ad;
  rd(N);
  {
    int Lj4PdHRW;
    for(Lj4PdHRW=(0);Lj4PdHRW<(N-1);Lj4PdHRW++){
      rd(A[Lj4PdHRW]);A[Lj4PdHRW] += (-1);
      rd(B[Lj4PdHRW]);B[Lj4PdHRW] += (-1);
      rd(C[Lj4PdHRW]);
    }
  }
  g.setEdge(N,N-1,A,B,C);
  g.g.getDist(0, dep);
  hld.init(g.g);
  t.init(&hld, NULL);
  tdis.init(&hld, NULL);
  for(i=(0);i<(N);i++){
    mn[i] = mn1[i] = mn2[i] = mn3[i] = updis[i] = 4611686016279904256LL;
  }
  for(i=(0);i<(N-1);i++){
    if(dep[A[i]] > dep[B[i]]){
      swap(A[i], B[i]);
    }
    chmin(mn3[A[i]], C[i]);
    if(mn1[A[i]] > mn2[A[i]]){
      swap(mn1[A[i]], mn2[A[i]]);
    }
    if(mn2[A[i]] > mn3[A[i]]){
      swap(mn2[A[i]], mn3[A[i]]);
    }
    if(mn1[A[i]] > mn2[A[i]]){
      swap(mn1[A[i]], mn2[A[i]]);
    }
    ;
    updis[B[i]] = C[i];
  }
  for(i=(0);i<(N-1);i++){
    if(mn1[A[i]] != C[i]){
      mn[B[i]] =mn1[A[i]];
    }
    else{
      mn[B[i]] =mn2[A[i]];
    }
  }
  for(i=(0);i<(N);i++){
    t.change(i,i,mn[i]);
  }
  for(i=(0);i<(N-1);i++){
    tdis.change(B[i],B[i],C[i]);
  }
  int hCmBdyQB = rd_int();
  for(a2conNHc=(0);a2conNHc<(hCmBdyQB);a2conNHc++){
    rd(X);X += (-1);
    rd(Y);Y += (-1);
    z = hld.lca(X, Y);
    res = 0;
    ad = 4611686016279904256LL;
    xx = yy = xxx = yyy = -1;
    if(X != z){
      xx = hld.up(X, dep[X] - dep[z] - 1);
    }
    if(Y != z){
      yy = hld.up(Y, dep[Y] - dep[z] - 1);
    }
    if(xx != -1 && xx != X){
      xxx = hld.up(dep[X] - dep[z] - 2);
    }
    if(yy != -1 && yy != Y){
      yyy = hld.up(dep[Y] - dep[z] - 2);
    }
    if(xx != -1){
      res += tdis.getSum(X, xx);
    }
    if(yy != -1){
      res += tdis.getSum(Y, yy);
    }
    chmin(ad, updis[z]);
    if(xx != -1){
      chmin(ad, mn1[X]);
    }
    if(yy != -1){
      chmin(ad, mn1[Y]);
    }
    if(xxx != -1){
      chmin(ad, t.getMinVal(X, xxx));
    }
    if(yyy != -1){
      chmin(ad, t.getMinVal(Y, yyy));
    }
    cand[0] = mn1[z];
    cand[1] = mn2[z];
    cand[2] = mn3[z];
    if(xx != -1){
      for(i=(0);i<(3);i++){
        if(cand[i]==updis[xx]){
          cand[i] = 4611686016279904256LL;
          break;
        }
      }
    }
    if(yy != -1){
      for(i=(0);i<(3);i++){
        if(cand[i]==updis[yy]){
          cand[i] = 4611686016279904256LL;
          break;
        }
      }
    }
    {
      int iMWUTgY_;
      long long AlM5nNnR;
      if(3==0){
        AlM5nNnR = 0;
      }
      else{
        AlM5nNnR = cand[0];
        for(iMWUTgY_=(1);iMWUTgY_<(3);iMWUTgY_++){
          AlM5nNnR = min_L(AlM5nNnR, cand[iMWUTgY_]);
        }
      }
      chmin(ad, AlM5nNnR);
    }
    if(ad == 4611686016279904256LL){
      wt_L(-1);
      wt_L('\n');
      continue;
    }
    wt_L(res + ad * 2);
    wt_L('\n');
  }
  return 0;
}
// cLay varsion 20200813-1 [beta]

// --- original code ---
// int N, A[1d5], B[1d5]; ll C[1d5];
// int X, Y;
// 
// wgraph<ll> g;
// HLD hld;
// HLD_segtree<ll> t, tdis;
// int dep[1d5];
// ll mn1[1d5], mn2[1d5], mn3[1d5], mn[1d5], updis[1d5];
// ll cand[3];
// 
// {
//   int xx, yy, xxx, yyy, z;
//   ll res, ad;
//   rd(N,(A--,B--,C)(N-1));
// 
//   g.setEdge(N,N-1,A,B,C);
//   g.g.getDist(0, dep);
//   hld.init(g.g);
//   t.init(&hld, NULL);
//   tdis.init(&hld, NULL);
// 
//   rep(i,N) mn[i] = mn1[i] = mn2[i] = mn3[i] = updis[i] = ll_inf;
//   rep(i,N-1){
//     if(dep[A[i]] > dep[B[i]]) swap(A[i], B[i]);
//     mn3[A[i]] <?= C[i];
//     sortE(mn1[A[i]], mn2[A[i]], mn3[A[i]]);
//     updis[B[i]] = C[i];
//   }
//   rep(i,N-1) mn[B[i]] = if[mn1[A[i]] != C[i], mn1[A[i]], mn2[A[i]]];
//   rep(i,N) t.change(i,i,mn[i]);
//   rep(i,N-1) tdis.change(B[i],B[i],C[i]);
// 
//   REP(rd_int()){
//     rd(X--, Y--);
//     z = hld.lca(X, Y);
// 
//     res = 0;
//     ad = ll_inf;
//     xx = yy = xxx = yyy = -1;
// 
//     if(X != z) xx = hld.up(X, dep[X] - dep[z] - 1);
//     if(Y != z) yy = hld.up(Y, dep[Y] - dep[z] - 1);
//     if(xx != -1 && xx != X) xxx = hld.up(dep[X] - dep[z] - 2);
//     if(yy != -1 && yy != Y) yyy = hld.up(dep[Y] - dep[z] - 2);
// 
// //    wt(z,":",X,xxx,xx,":",Y,yyy,yy);
// 
//     if(xx != -1) res += tdis.getSum(X, xx);
//     if(yy != -1) res += tdis.getSum(Y, yy);
// 
//     ad <?= updis[z];
//     if(xx != -1) ad <?= mn1[X];
//     if(yy != -1) ad <?= mn1[Y];
//     if(xxx != -1) ad <?= t.getMinVal(X, xxx);
//     if(yyy != -1) ad <?= t.getMinVal(Y, yyy);
// 
//     cand[0] = mn1[z];
//     cand[1] = mn2[z];
//     cand[2] = mn3[z];
//     if(xx != -1) rep(i,3) if(cand[i]==updis[xx]) cand[i] = ll_inf, break;
//     if(yy != -1) rep(i,3) if(cand[i]==updis[yy]) cand[i] = ll_inf, break;
//     ad <?= min(cand(3));
// 
//     if(ad == ll_inf) wt(-1), continue;
//     wt(res + ad * 2);
//   }
// }