Problem: Akira, the student council president of A High School, decided to investigate which club activities the A High School students belong to. A High School has N students numbered 1 to N and M types of club activities numbered 1 to M. There is no limit to the number of people in each club activity, and there can be 0 club activities. However, according to the school rules of A High School, students can only belong to one club activity. All students follow this school rule.

Akira asked student members to investigate and obtained records for line K, such as each line being one of the following:

* Student a and student b belong to the same club activities.
* Student c belongs to club activity x.



However, there may be a contradiction in this record that would cause someone to violate school rules. Akira decided to look at the first line in order and look for the first line that could be judged to be inconsistent.

Create a program that finds the number of the first line that can be determined to be inconsistent given a record of K lines.



Input

The input is given in the following format.


NMK
record1
record2
::
recordK


The first line gives the number of students N (1 ≤ N ≤ 100000), the number of club activity types M (1 ≤ M ≤ 100000), and the number of recorded lines K (1 ≤ K ≤ 200000). Each line of record, recordi, is given in the following K lines in one of the following formats:


1 a b


Or


2 c x


When the first digit is "1", it indicates that student a (1 ≤ a ≤ N) and student b (1 ≤ b ≤ N) belong to the same club activity. However, a ≠ b.

When the first digit is "2", it indicates that student c (1 ≤ c ≤ N) belongs to club activity x (1 ≤ x ≤ M).

Output

Output the number of the first line that can be determined to be inconsistent on one line. If not found, output 0 on one line.

Examples

Input

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


Output

4


Input

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


Output

0


Input

3 2 2
1 1 2
2 1 1


Output

0

Solution (in CPP):

Solution:

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

// pp basics

#define in ,
#define esc_paren(...) __VA_ARGS__
#define pp_empty(...)
#define pp_cat_i(x, y) x ## y
#define pp_cat(x, y) pp_cat_i(x, y)

#define pp_inc0 1
#define pp_inc1 2
#define pp_inc2 3
#define pp_inc3 4
#define pp_inc4 5
#define pp_inc5 6
#define pp_inc6 7
#define pp_inc7 8
#define pp_inc8 9
#define pp_inc(i) pp_cat(pp_inc, i)

// pp args counter

// #define def_pp_comma0 ,1 pp_empty
// #define pp_comma0 ,0
// #define pp_is_empty(x, ...) pp_is_empty1(x pp_comma0)
// #define pp_is_empty1(x) pp_is_empty2((def_ ## x))
// #define pp_is_empty2(t) pp_is_empty3 t
// #define pp_is_empty3(f, s) s

#define pp_arg10(_0, _1, _2, _3, _4, _5, _6, _7, _8, _9, ...) _9
#define pp_has_comma(...) pp_arg10(__VA_ARGS__, 1, 1, 1, 1, 1, 1, 1, 1, 0)
#define pp_trigger_paren(...) ,
#define pp_is_empty(...) \
  pp_is_empty1( \
      pp_has_comma(__VA_ARGS__), \
      pp_has_comma(pp_trigger_paren __VA_ARGS__), \
      pp_has_comma(__VA_ARGS__()), \
      pp_has_comma(pp_trigger_paren __VA_ARGS__()) \
      ) 
#define pp_paste5(_0, _1, _2, _3, _4) _0 ## _1 ## _2 ## _3 ## _4
#define pp_is_empty1(_0, _1, _2, _3) pp_has_comma(pp_paste5(pp_is_empty_case_, _0, _1, _2, _3))
#define pp_is_empty_case_0001 ,

#define pp_is_one(...) pp_is_one_(__VA_ARGS__, pp_one_seq)
#define pp_is_one_(...) pp_is_one_n(__VA_ARGS__)
#define pp_is_one_n(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10, N, ...) N
#define pp_one_seq 0,0,0,0,0,0,0,0,0,1,0

#define pp_narg(...) \
  pp_narg_(__VA_ARGS__, pp_narg_seq)
#define pp_narg_(...) \
  pp_arg_n(__VA_ARGS__)
#define pp_narg_n( \
    _1, _2, _3, _4, _5, _6, _7, _8, _9,_10, \
    _11,_12,_13,_14,_15,_16,_17,_18,_19,_20, \
    _21,_22,_23,_24,_25,_26,_27,_28,_29,_30, \
    _31,_32,_33,_34,_35,_36,_37,_38,_39,_40, \
    _41,_42,_43,_44,_45,_46,_47,_48,_49,_50, \
    _51,_52,_53,_54,_55,_56,_57,_58,_59,_60, \
    _61,_62,_63,n,...) n
#define pp_narg_seq \
  63,62,61,60, \
59,58,57,56,55,54,53,52,51,50, \
49,48,47,46,45,44,43,42,41,40, \
39,38,37,36,35,34,33,32,31,30, \
29,28,27,26,25,24,23,22,21,20, \
19,18,17,16,15,14,13,12,11,10, \
9, 8, 7, 6, 5, 4, 3, 2, 1, 0

// pp if
#define pp_if_0(x, y) y
#define pp_if_1(x, y) x
#define pp_if(cond, x, y) pp_cat(pp_if_, cond)(x, y)

// pp foreach
#define pp_foreach_i9(i, f, x, ...) f(x) pp_if(pp_is_empty(__VA_ARGS__), pp_empty, pp_cat(pp_foreach_i, i))(pp_inc(i), f, __VA_ARGS__)
#define pp_foreach_i8(i, f, x, ...) f(x) pp_if(pp_is_empty(__VA_ARGS__), pp_empty, pp_cat(pp_foreach_i, i))(pp_inc(i), f, __VA_ARGS__)
#define pp_foreach_i7(i, f, x, ...) f(x) pp_if(pp_is_empty(__VA_ARGS__), pp_empty, pp_cat(pp_foreach_i, i))(pp_inc(i), f, __VA_ARGS__)
#define pp_foreach_i6(i, f, x, ...) f(x) pp_if(pp_is_empty(__VA_ARGS__), pp_empty, pp_cat(pp_foreach_i, i))(pp_inc(i), f, __VA_ARGS__)
#define pp_foreach_i5(i, f, x, ...) f(x) pp_if(pp_is_empty(__VA_ARGS__), pp_empty, pp_cat(pp_foreach_i, i))(pp_inc(i), f, __VA_ARGS__)
#define pp_foreach_i4(i, f, x, ...) f(x) pp_if(pp_is_empty(__VA_ARGS__), pp_empty, pp_cat(pp_foreach_i, i))(pp_inc(i), f, __VA_ARGS__)
#define pp_foreach_i3(i, f, x, ...) f(x) pp_if(pp_is_empty(__VA_ARGS__), pp_empty, pp_cat(pp_foreach_i, i))(pp_inc(i), f, __VA_ARGS__)
#define pp_foreach_i2(i, f, x, ...) f(x) pp_if(pp_is_empty(__VA_ARGS__), pp_empty, pp_cat(pp_foreach_i, i))(pp_inc(i), f, __VA_ARGS__)
#define pp_foreach_i1(i, f, x, ...) f(x) pp_if(pp_is_empty(__VA_ARGS__), pp_empty, pp_cat(pp_foreach_i, i))(pp_inc(i), f, __VA_ARGS__)
#define pp_foreach_i0(i, f, x, ...) f(x) pp_if(pp_is_empty(__VA_ARGS__), pp_empty, pp_cat(pp_foreach_i, i))(pp_inc(i), f, __VA_ARGS__)
#define pp_foreach_i(i, f, ...) pp_if(pp_is_empty(__VA_ARGS__), pp_empty, pp_cat(pp_foreach_i, i))(pp_inc(i), f, __VA_ARGS__)
#define pp_foreach(f, ...) pp_foreach_i(0, f, __VA_ARGS__)

// alternative rep macro
#define rep(...) rep1(rep2, (__VA_ARGS__))
#define rep1(X, A) X A
#define rep2(i, ...) pp_if(pp_is_one(__VA_ARGS__), rep_len1(i, __VA_ARGS__), rep3(i, __VA_ARGS__))
#define rep_len1(i, end, ...) for (int i = 0; i < end; i++)
#define rep3(i, iter, ...) rep4(rep5, (iter, i, esc_paren __VA_ARGS__))
#define rep4(X, A) X A
#define rep5(iter, ...) iter(__VA_ARGS__)

// iterators
#define up up_iter ,
#define up_iter3(i, start, end) for (int i = start; i < end; i++)
#define up_iter4(i, start, end, up) for (int i = start; i < end; i += up)
#define up_iter(...) CAT(up_iter, PP_NARG(__VA_ARGS__))(__VA_ARGS__)
#define down down_iter ,
#define down_iter2(i, end) for(int i = end-1; i >= 0; i++)
#define down_iter3(i, start, end) for (int i = end-1; i >= start; i--)
#define down_iter4(i, start, end, down) for (int i = end-1; i >= start; i -= down)
#define down_iter(...) CAT(down_iter, PP_NARG(__VA_ARGS__))(__VA_ARGS__)
#define viter viter_iter ,
#define viter_iter(i, v) auto tmpitr=v.begin(); for (auto i=*tmpitr; tmpitr != v.end(); tmpitr++)

// debug macros
#define debug_var_elem(v) << #v << "=" << v << " "
#ifdef DEBUG
#define debug_echo(e) cout << "L" << __LINE__ << ": " << e << endl
#define debug_var(...) cout << "L" << __LINE__ << ": " pp_foreach(debug_var_elem, __VA_ARGS__) << endl
#else
#define debug_echo(e)
#define debug_var(...)
#endif

// short names
typedef long long ll;
#define down_queue(x) priority_queue<x>
#define up_queue(x) priority_queue<x, vector<x>, greater<x>>
ll gcd(ll a,ll b){while(b){ll tmp = a % b;a = b;b = tmp;}return a;}
ll lcm(ll a,ll b){return a / gcd(a,b) * b;}
#define all(x) x.begin(), x.end()
#define split_str(str, sp_word) istringstream stream(str); string res; for(int cnt = 0; getline(stream,res,sp_word); cnt++)
#define digit(x) ((int)log10((double)(x)) + 1)
#define mp(x,y) make_pair(x,y)
#define pb(x) push_back(x)
#define pf(x) push_front(x)
#define vec_cpy(to,from) copy(all(to),back_inserter(from))
#define ary_cpy(to,from) memcpy(to, from, sizeof(from))
#define MOD 1000000007 

//
// Implementation

#define pp_gen_field(list) pp_gen_field1 list
#define pp_gen_field1(name, val) decltype(val) name;
#define pp_gen_init(list) pp_gen_init1 list
#define pp_gen_init1(name, val) ,val
#define pp_gen_find_set_wrap(ufnodename) ufnodename pp_gen_find_set
#define pp_gen_find_set(list) pp_gen_find_set1 list
#define pp_gen_find_set1(name, val) \
  find_set_ ## name(int x, decltype(val) v) { \
    if (nodes[x].parent == x) { \
      nodes[x].name = v; \
      return nodes[x]; \
    } else { \
      return nodes[x] = find_set_ ## name(nodes[x].parent, v); \
    } \
  }
#define pp_gen_unite_set(list) pp_gen_unite_set1 list
#define pp_gen_unite_set1(name, val) \
  if (nodes[x].name == val) { \
    find_set_ ## name(x, find(y).name); \
  } \
  if (nodes[y].name == val) { \
    find_set_ ## name(y, find(x).name); \
  }

#define def_unionfind(ufname, ufnodename, ...) \
  struct ufnodename { \
    int parent; \
    pp_foreach(pp_gen_field, __VA_ARGS__) \
  }; \
  struct ufname { \
    vector<ufnodename> nodes; \
    vector<int> rank; \
    ufname(int n) : nodes(n+1), rank(n+1) { \
      rep (i in n) { \
        nodes[i] = ufnodename{i pp_foreach(pp_gen_init, __VA_ARGS__)}; \
        rank[i] = 0; \
      } \
    } \
    ufnodename find(int x) { \
      if (nodes[x].parent == x) { \
        return nodes[x]; \
      } else { \
        return nodes[x] = find(nodes[x].parent); \
      } \
    } \
    pp_foreach(pp_gen_find_set_wrap(ufnodename), __VA_ARGS__) \
    void unite(int x, int y) { \
      x = find(x).parent; \
      y = find(y).parent; \
      if (x == y) return; \
      if (rank[x] < rank[y]) { \
        pp_foreach(pp_gen_unite_set, __VA_ARGS__); \
        nodes[x].parent = y; \
      } else { \
        pp_foreach(pp_gen_unite_set, __VA_ARGS__); \
        nodes[y].parent = x; \
        if (rank[x] == rank[y]) rank[x]++; \
      } \
    } \
    bool same(int x, int y) { \
      return find(x).parent == find(y).parent; \
    } \
  }

def_unionfind(UFClub, UFClubNode, (club in -1));

int N, M, K;

int main() {
  cin >> N >> M >> K;
  UFClub uf(N);
  rep (i in K) {
    int t; cin >> t;
    int a, b; cin >> a >> b;
    if (t == 1) {
      auto af = uf.find(a);
      auto bf = uf.find(b);
      if (af.club == -1 || bf.club == -1) {
        // discard
      } else if (af.club != bf.club) {
        cout << i+1 << endl;
        return 0;
      }
      uf.unite(a, b);
    } else {
      int aclub = uf.find(a).club;
      debug_var(aclub, b);
      if (aclub == -1) {
        uf.find_set_club(a, b);
      } else if (aclub != b) {
        cout << i+1 << endl;
        return 0;
      }
    }
  }
  cout << 0 << endl;
}