#include<bits/stdc++.h>
using namespace std;
void *wmem;
void rd(int &x){
  int k, m=0;
  x=0;
  for(;;){
    k = getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
void wt_L(int x){
  char f[10];
  int m=0, s=0;
  if(x<0){
    m=1;
    x=-x;
  }
  while(x){
    f[s++]=x%10;
    x/=10;
  }
  if(!s){
    f[s++]=0;
  }
  if(m){
    putchar_unlocked('-');
  }
  while(s--){
    putchar_unlocked(f[s]+'0');
  }
}
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 S, class T> inline S chmin(S &a, T b){
  if(a>b){
    a=b;
  }
  return a;
}
template<class T> struct segtree{
  T *addval, *fixval, *mn, *sum;
  char *fixed;
  int N, logN, *mnind;
  void malloc(int maxN, int once = 0){
    int i;
    for(i=1;i<maxN;i*=2){
      ;
    }
    sum = (T*)std::malloc(sizeof(T)*2*i);
    mn = (T*)std::malloc(sizeof(T)*2*i);
    mnind = (int*)std::malloc(sizeof(T)*2*i);
    fixval = (T*)std::malloc(sizeof(T)*i);
    addval = (T*)std::malloc(sizeof(T)*i);
    fixed = (char*)std::malloc(sizeof(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){
      ;
    }
    sum = (T*)(*mem);
    mn = sum + 2*i;
    mnind = (int*)(mn + 2*i);
    fixval = (T*)(mnind + 2*i);
    addval = fixval + i;
    fixed = (char*)(addval + i);
    *mem = fixed + i;
    if(once){
      setN(maxN);
    }
  }
  void free(void){
    std::free(sum);
    std::free(mn);
    std::free(mnind);
    std::free(fixval);
    std::free(addval);
    std::free(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];
      }
    }
    for(i=1;i<N;i++){
      fixed[i] = 0;
    }
    for(i=1;i<N;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 aa=a - N, i, nd, st, sz;
    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 st=a - N, sz=1;
    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 aa, bb, st_a=a, st_b=b, sz=1;
    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 aa, bb, sz=1;
    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){
    int sz=1;
    pair<T,int> res;
    a += N;
    b += N;
    push(a);
    push(b-1);
    res.first = numeric_limits<T>::max();
    res.second = -1;
    while(a < b){
      if(a%2){
        chmin(res, make_pair(mn[a], mnind[a]));
        a++;
      }
      if(b%2){
        b--;
        chmin(res, make_pair(mn[b], mnind[b]));
      }
      a /= 2;
      b /= 2;
    }
    return res;
  }
  inline T getMinVal(int a, int b){
    return getMin(a,b).first;
  }
  inline int getMinInd(int a, int b){
    return getMin(a,b).second;
  }
  inline T getSum(int a, int b){
    T res;
    int sz=1;
    a += N;
    b += N;
    push(a);
    push(b-1);
    res = 0;
    while(a < b){
      if(a%2){
        res += sum[a++];
      }
      if(b%2){
        res += sum[--b];
      }
      a /= 2;
      b /= 2;
    }
    return res;
  }
}
;
struct graph{
  int N, **edge, *es;
  void setEdge(int N__, int M, int A[], int B[], void **mem = &wmem){
    int i;
    N = N__;
    es = (int*)(*mem);
    edge = (int**)(es+N);
    edge[0] = (int*)(edge+N);
    for(i=0;i<N;i++){
      es[i] = 0;
    }
    for(i=0;i<M;i++){
      es[A[i]]++;
      es[B[i]]++;
    }
    for(i=1;i<N;i++){
      edge[i] = edge[i-1] + es[i-1];
    }
    (*mem) = edge[N-1] + es[N-1];
    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 setDirectEdge(int N__, int M, int A[], int B[], void **mem = &wmem){
    int i;
    N = N__;
    es = (int*)(*mem);
    edge = (int**)(es+N);
    edge[0] = (int*)(edge+N);
    for(i=0;i<N;i++){
      es[i] = 0;
    }
    for(i=0;i<M;i++){
      es[A[i]]++;
    }
    for(i=1;i<N;i++){
      edge[i] = edge[i-1] + es[i-1];
    }
    (*mem) = edge[N-1] + es[N-1];
    for(i=0;i<N;i++){
      es[i] = 0;
    }
    for(i=0;i<M;i++){
      edge[A[i]][es[A[i]]++] = B[i];
    }
  }
  graph reverse(void **mem = &wmem){
    graph g;
    int i, j, k;
    g.N = N;
    g.es = (int*)(*mem);
    g.edge = (int**)(g.es + N);
    g.edge[0] = (int*)(g.edge + N);
    for(i=0;i<N;i++){
      g.es[i] = 0;
    }
    for(i=0;i<N;i++){
      for(j=0;j<es[i];j++){
        g.es[edge[i][j]]++;
      }
    }
    for(i=1;i<N;i++){
      g.edge[i] = g.edge[i-1] + g.es[i-1];
    }
    *mem = g.edge[N-1] + g.es[N-1];
    for(i=0;i<N;i++){
      g.es[i] = 0;
    }
    for(i=0;i<N;i++){
      for(j=0;j<es[i];j++){
        k = edge[i][j];
        g.edge[k][g.es[k]++] = i;
      }
    }
    return g;
  }
  graph reduce(int tn, int ind[], int self_e = 0, int dep_e = 0, void **mem = &wmem){
    graph g;
    int M=0, i, j, k, x, y;
    pair<int,int> *A;
    for(i=0;i<N;i++){
      M += es[i];
    }
    A = (pair<int,int>*)((int*)((int**)(*mem) + tn) + tn + M);
    M = 0;
    for(i=0;i<N;i++){
      x = ind[i];
      if(x < 0){
        continue;
      }
      for(j=0;j<es[i];j++){
        y = ind[edge[i][j]];
        if(y < 0){
          continue;
        }
        if(self_e==0 && x==y){
          continue;
        }
        A[M++] = make_pair(x, y);
      }
    }
    if(dep_e==0){
      sort(A, A+M);
      k = 0;
      for(i=0;i<M;i++){
        if(k && A[k-1]==A[i]){
          continue;
        }
        A[k++] = A[i];
      }
      M = k;
    }
    g.N = tn;
    g.es = (int*)(*mem);
    g.edge = (int**)(g.es + tn);
    g.edge[0] = (int*)(g.edge + tn);
    for(i=0;i<tn;i++){
      g.es[i] = 0;
    }
    for(i=0;i<M;i++){
      g.es[A[i].first]++;
    }
    for(i=1;i<tn;i++){
      g.edge[i] = g.edge[i-1] + g.es[i-1];
    }
    *mem = g.edge[tn-1] + g.es[tn-1];
    for(i=0;i<tn;i++){
      g.es[i] = 0;
    }
    for(i=0;i<M;i++){
      j = A[i].first;
      k = A[i].second;
      g.edge[j][g.es[j]++] = k;
    }
    return g;
  }
  void getDist(int root, int res[], void *mem = wmem){
    int i, j, k, *q, s, z;
    q=(int*)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;
      }
    }
  }
  inline int sccDFS(int num[], int st, int mx){
    int i, j;
    num[st]=-2;
    for(i=0;i<es[st];i++){
      j=edge[st][i];
      if(num[j]==-1){
        mx=sccDFS(num,j,mx);
      }
    }
    num[st]=mx;
    return mx+1;
  }
  int scc(int res[], void *mem = wmem){
    graph r;
    int i, j, k, *nrv, *num, ret=0, *st, st_size;
    r = reverse(&mem);
    st = (int*)mem;
    num = st+N;
    nrv = num + N;
    for(i=0;i<N;i++){
      res[i] = num[i] = -1;
    }
    k = 0;
    for(i=0;i<N;i++){
      if(num[i]==-1){
        k = sccDFS(num,i,k);
      }
    }
    for(i=0;i<N;i++){
      nrv[num[i]] = i;
    }
    for(k=N-1;k>=0;k--){
      i=nrv[k];
      if(res[i]>=0){
        continue;
      }
      res[i]=ret;
      st_size=0;
      st[st_size++]=i;
      while(st_size){
        i=st[--st_size];
        for(j=0;j<r.es[i];j++){
          if(res[r.edge[i][j]]==-1){
            res[r.edge[i][j]]=ret;
            st[st_size++]=r.edge[i][j];
          }
        }
      }
      ret++;
    }
    return ret;
  }
  inline void bccDFS(int v, int u, int *res, int *rt, int &rts, int *S, int &Ss, int *inS, int *num, int &tm){
    int i, k;
    num[v] = ++tm;
    S[Ss++] = v;
    inS[v] = 1;
    rt[rts++] = v;
    for(i=0;i<es[v];i++){
      int w=edge[v][i];
      if(!num[w]){
        bccDFS(w, v, res, rt, rts, S, Ss, inS, num, tm);
      }
      else if(u != w && inS[w]){
        while(num[rt[rts-1]] > num[w]){
          rts--;
        }
      }
    }
    if(v == rt[rts-1]){
      k = S[Ss-1];
      for(;;){
        int w=S[--Ss];
        inS[w] = 0;
        res[w] = k;
        if(v==w){
          break;
        }
      }
      rts--;
    }
  }
  int bcc(int res[], void *mem=wmem){
    int *S, Ss=0, i, *inS, k, *num, *rt, rts=0, tm=0;
    pair<int,int> *arr;
    num = (int*)mem;
    rt = num + N;
    S = rt + N;
    inS = S + N;
    memset(num, 0, sizeof(int)*N);
    memset(inS, 0, sizeof(int)*N);
    for(i=0;i<N;i++){
      if(!num[i]){
        bccDFS(i, N, res, rt, rts, S, Ss, inS, num, tm);
      }
    }
    arr = (pair<int,int>*)mem;
    for(i=0;i<N;i++){
      arr[i].first = res[i];
      arr[i].second = i;
    }
    sort(arr, arr+N);
    k = 0;
    for(i=0;i<N;i++){
      if(i && arr[i].first != arr[i-1].first){
        k++;
      }
      res[arr[i].second] = k;
    }
    return k+1;
  }
}
;
struct HLD{
  int N, **edge, *es, *group, *groupDepth, **groupNode, groupNum, *groupSize, *groupUpNode, *groupind;
  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){
    char *vis;
    int i, j, k, mx, *q, q_ed, q_st, *sz, x, y;
    N = N__;
    es = es__;
    edge = edge__;
    group = (int*)(*mem);
    groupind = group + N;
    *mem = groupind + N;
    q = (int*)(*mem);
    sz = q + N;
    vis = (char*)(sz + N);
    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];
      }
    }
    groupSize = (int*)(*mem);
    groupUpNode = groupSize + groupNum;
    groupDepth = groupUpNode + groupNum;
    for(i=0;i<groupNum;i++){
      groupSize[i] = 0;
    }
    for(i=0;i<N;i++){
      groupSize[group[i]]++;
    }
    groupNode = (int**)(groupDepth + groupNum);
    groupNode[0] = (int*)(groupNode + groupNum);
    for(i=1;i<groupNum;i++){
      groupNode[i] = groupNode[i-1] + groupSize[i-1];
    }
    *mem = groupNode[groupNum-1] + groupSize[groupNum-1];
    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, x2, y1, 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 res=0, x1, x2;
    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 res=0, x1, x2, y1, y2;
    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], x2=groupind[x];
    if(x2==0){
      return groupUpNode[x1];
    }
    return groupNode[x1][x2-1];
  }
  int up(int x, int d){
    int x1=group[x], 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, j;
    hld = hld__;
    seg = (segtree<T>*)(*mem);
    *mem = seg + hld->groupNum;
    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, ui, vg, 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, ui, vg, 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){
    int ug, ui, vg, vi;
    pair<T,int> res, tmp;
    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, ui, vg, 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;
  }
}
;
char memarr[64000000];
int A[200000], B[200000], M, N, Q, X, Y, Z, cnv[100000], tn, val[100000];
priority_queue<int> q[100000];
int main(){
  HLD hld;
  HLD_segtree<int> t;
  graph g, og;
  int i, j, k;
  wmem = memarr;
  rd(N);
  rd(M);
  rd(Q);
  {
    int Lj4PdHRW;
    for(Lj4PdHRW=0;Lj4PdHRW<M;Lj4PdHRW++){
      rd(A[Lj4PdHRW]);
      rd(B[Lj4PdHRW]);
    }
  }
  {
    int KL2GvlyY;
    for(KL2GvlyY=0;KL2GvlyY<(M-1) + 1;KL2GvlyY++){
      A[KL2GvlyY]--;
    }
  }
  {
    int Q5VJL1cS;
    for(Q5VJL1cS=0;Q5VJL1cS<(M-1) + 1;Q5VJL1cS++){
      B[Q5VJL1cS]--;
    }
  }
  og.setEdge(N,M,A,B);
  tn = og.bcc(cnv);
  g = og.reduce(tn, cnv);
  {
    int e98WHCEY;
    for(e98WHCEY=0;e98WHCEY<(tn-1) + 1;e98WHCEY++){
      val[e98WHCEY] = 1;
    }
  }
  hld.init(g);
  t.init(&hld, val);
  {
    int cTE1_r3A;
    for(cTE1_r3A=0;cTE1_r3A<(tn-1) + 1;cTE1_r3A++){
      val[cTE1_r3A] = -1;
    }
  }
  while(Q--){
    rd(X);
    rd(Y);
    rd(Z);
    if(X==1){
      Y = cnv[Y-1];
      q[Y].push(Z);
      if(val[Y] < Z){
        val[Y] = Z;
        t.change(Y,Y,-Z);
      }
    }
    else{
      Y = cnv[Y-1];
      Z = cnv[Z-1];
      k = t.getMinInd(Y, Z);
      wt_L(val[k]);
      putchar_unlocked('\n');
      if(val[k]==-1){
        continue;
      }
      q[k].pop();
      if(q[k].size()){
        Z = q[k].top();
      }
      else{
        Z = -1;
      }
      val[k] = Z;
      t.change(k,k,-Z);
    }
  }
  return 0;
}
// cLay varsion 20170628-1

// --- original code ---
// int N, M, Q;
// int A[200000], B[200000];
// int X, Y, Z;
// 
// int tn;
// int cnv[100000];
// int val[100000];
// priority_queue<int> q[100000];
// {
//   int i, j, k;
//   graph og, g;
//   HLD hld;
//   HLD_segtree<int> t;
//   
//   rd(N,M,Q,(A,B)(M));
//   A[0..M-1]--;
//   B[0..M-1]--;
//   og.setEdge(N,M,A,B);
//   tn = og.bcc(cnv);
//   g = og.reduce(tn, cnv);
// 
//   val[0..tn-1] = 1;
//   hld.init(g);
//   t.init(&hld, val);
//   val[0..tn-1] = -1;
// 
//   while(Q--){
//     rd(X,Y,Z);
//     if(X==1){
//       Y = cnv[Y-1];
//       q[Y].push(Z);
//       if(val[Y] < Z){
//         val[Y] = Z;
//         t.change(Y,Y,-Z);
//       }
//     } else {
//       Y = cnv[Y-1];
//       Z = cnv[Z-1];
//       k = t.getMinInd(Y, Z);
//       wt(val[k]);
//       if(val[k]==-1) continue;
//       q[k].pop();
//       if(q[k].size()) Z = q[k].top(); else Z = -1;
//       val[k] = Z;
//       t.change(k,k,-Z);
//     }
//   }
// }