/**
 * author:  tsuyu93
 * started: 2021-06-06  01:10:32
 * 継続は力なり、雨だれ石を穿つ
 * make the impossible possible
**/

#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>

// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mpb = boost::multiprecision;
// using bint = mpb::cpp_int;
// // 仮数部が1024ビットの浮動小数点数型(TLEしたら小さくする)
// using Real = mpb::number<mpb::cpp_dec_float<1024>>;

#ifdef __HOGE__
#pragma region macro
#endif
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned;
using pll = pair<ll, ll>;
using pli = pair<ll, int>;
using pii = pair<int, int>;
using pld = pair<ll, ld>;
using ppiii =  pair<pii, int>;
using ppiill = pair<pii, ll>;
using ppllll = pair<pll, ll>;
using pplii = pair<pli, int>;
using mii = map<int, int>;
using dll = deque<ll>;
using qll = queue<ll>;
using pqll = priority_queue<ll>;
using pqrll = priority_queue<ll, vector<ll>, greater<ll>>;
using pqrpll = priority_queue<pll, vector<pll>, greater<pll>>;
using vint = vector<int>;
using vbool = vector<bool>;
using vstr = vector<string>;
using vll = vector<ll>;
using vld = vector<ld>;
using vpll = vector<pll>;
using vvll = vector<vector<ll>>;
using vvint = vector<vector<int>>;
using vvld = vector<vector<ld>>;
using vvbool = vector<vbool>;
using vvstr = vector<vstr>;
using vvpll = vector<vector<pll>>;
#define REP(i,n) for(ll i=0;i<ll(n);i++)
#define REPD(i,n) for(ll i=n-1;i>=0;i--)
#define FOR(i,a,b) for(ll i=a;i<=ll(b);i++)
#define FORD(i,a,b) for(ll i=a;i>=ll(b);i--)
#define overload4(_1,_2,_3,_4,name,...) name
#define overload3(_1,_2,_3,name,...) name
#define rep1(n) for(ll i=0;i<n;++i)
#define rep2(i,n) for(ll i=0;i<n;++i)
#define rep3(i,a,b) for(ll i=a;i<b;++i)
#define rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i=n;i--;)
#define rrep2(i,n) for(ll i=n;i--;)
#define rrep3(i,a,b) for(ll i=b;i-->(a);)
#define rrep4(i,a,b,c) for(ll i=(a)+((b)-(a)-1)/(c)*(c);i>=(a);i-=c)
#define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define each1(i,a) for(auto&&i:a)
#define each2(x,y,a) for(auto&&[x,y]:a)
#define each3(x,y,z,a) for(auto&&[x,y,z]:a)
#define each(...) overload4(__VA_ARGS__,each3,each2,each1)(__VA_ARGS__)
#define all1(i) begin(i),end(i)
#define all2(i,a) begin(i),begin(i)+a
#define all3(i,a,b) begin(i)+a,begin(i)+b
#define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__)
#define rall1(i) (i).rbegin(),(i).rend()
#define rall2(i,k) (i).rbegin(),(i).rbegin()+k
#define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__)
#define SUM(...) accumulate(all(__VA_ARGS__),0LL)
#define ALL(x) x.begin(),x.end() 
#define rALL(x) x.rbegin(),x.rend() 
#define SIZE(x) ll(x.size()) 
#define Sort(a) sort(all(a))
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)int scan(){ return getchar(); }
#define fs first
#define sc second
#define endl '\n'
#define elif else if
#define ADD_OVERFLOW(a, b) __builtin_add_overflow_p (a, b, (decltype((a)+(b))) 0)
#define SUB_OVERFLOW(a, b) __builtin_sub_overflow_p (a, b, (decltype((a)+(b))) 0)
#define MUL_OVERFLOW(a, b) __builtin_mul_overflow_p (a, b, (decltype((a)+(b))) 0)
void scan(int& a){ scanf("%d", &a); }
void scan(unsigned& a){ scanf("%u", &a); }
void scan(long& a){ scanf("%ld", &a); }
void scan(long long& a){ scanf("%lld", &a); }
void scan(unsigned long long& a){ scanf("%llu", &a); }
void scan(char& a){ do{ a = getchar(); }while(a == ' ' || a == '\n'); }
void scan(float& a){ scanf("%f", &a); }
void scan(double& a){ scanf("%lf", &a); }
void scan(long double& a){ scanf("%Lf", &a); }
void scan(vector<bool>& a){ for(unsigned i = 0; i < a.size(); i++){ int b; scan(b); a[i] = b; } }
void scan(char a[]){ scanf("%s", a); }
void scan(string& a){ cin >> a; }
template<class T> void scan(vector<T>&);
template<class T, size_t size> void scan(array<T, size>&);
template<class T, class L> void scan(pair<T, L>&);
template<class T, size_t size> void scan(T(&)[size]);
template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); }
template<class T> void scan(deque<T>& a){ for(auto&& i : a) scan(i); }
template<class T, size_t size> void scan(array<T, size>& a){ for(auto&& i : a) scan(i); }
template<class T, class L> void scan(pair<T, L>& p){ scan(p.first); scan(p.second); }
template<class T, size_t size> void scan(T (&a)[size]){ for(auto&& i : a) scan(i); }
template<class T> void scan(T& a){ cin >> a; }
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); }
void print(){ putchar(' '); }
void print(bool a){ printf("%d", a); }
void print(int a){ printf("%d", a); }
void print(unsigned a){ printf("%u", a); }
void print(long a){ printf("%ld", a); }
void print(long long a){ printf("%lld", a); }
void print(unsigned long long a){ printf("%llu", a); }
void print(char a){ printf("%c", a); }
void print(char a[]){ printf("%s", a); }
void print(const char a[]){ printf("%s", a); }
void print(float a){ printf("%.15f", a); }
void print(double a){ printf("%.15f", a); }
void print(long double a){ printf("%.15Lf", a); }
void print(const string& a){ for(auto&& i : a) print(i); }
template<class T> void print(const complex<T>& a){ if(a.real() >= 0) print('+'); print(a.real()); if(a.imag() >= 0) print('+'); print(a.imag()); print('i'); }
template<class T> void print(const vector<T>&);
template<class T, size_t size> void print(const array<T, size>&);
template<class T, class L> void print(const pair<T, L>& p);
template<class T, size_t size> void print(const T (&)[size]);
template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T> void print(const deque<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> void print(const array<T, size>& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> void print(const pair<T, L>& p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } }
template<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
template <class T> vector<T> make_vec(size_t a, T b) {return vector<T>(a, b);}
template <class T, class... Ts> auto make_vec(size_t a, Ts... ts) {return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));}
#ifdef DEBUG
inline ll __lg(ull x){ return 63 - __builtin_clzll(x); }
#define debug(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); }
#else
#define debug(...) void(0)
#endif
#define INF32 2147483647 //2.147483647x10^{9}:32bit整数のinf
#define INF64 9223372036854775807 //9.223372036854775807x10^{18}:64bit整数のinf
const ll MOD = 1000000007;
const int inf = 1e9;
const ll INF = (1LL<<61);
const ll MAXR = 100000; //10^5:配列の最大のrange
const ld PI = acos(-1);
inline void Yes(bool b = true) { cout << (b ? "Yes" : "No") << '\n'; }
inline void YES(bool b = true) { cout << (b ? "YES" : "NO") << '\n'; }
inline void OKNG(bool b = true) { cout << (b ? "OK" : "NG") << '\n'; }
inline void GAme(bool b = true) { cout << (b ? "First" : "Second") << '\n'; }
inline void gAme(bool b = true) { cout << (b ? "first" : "second") << '\n'; }
inline void Takahashi_Aoki(bool b = true) { cout << (b ? "Takahashi" : "Aoki") << '\n'; }
inline void takahashi_aoki(bool b = true) { cout << (b ? "takahashi" : "aoki") << '\n'; }
inline void possible(bool i = true){ cout << (i?"possible":"impossible") << '\n'; }
inline void Possible(bool i = true){ cout << (i?"Possible":"Impossible") << '\n'; }
inline void POSSIBLE(bool i = true){ cout << (i?"POSSIBLE":"IMPOSSIBLE") << '\n'; }
template<typename A, typename B> inline bool chmin(A& a, B b) {if (a > b) {a = b;return true;}return false;}
template<typename A, typename B> inline bool chmax(A& a, B b) {if (a < b) {a = b;return true;}return false;}
template<class T> auto min(const T& a){ return *min_element(a.begin(),a.end()); }
template<class T> auto max(const T& a){ return *max_element(a.begin(),a.end()); }
template<typename T> T power(T a, T b) {T res=1;while (b>0) {if (b&1){res*=a;}b/=2;a*=a;}return res;}
long long powmod(long long a, long long b) {long long res=1;while (b>0) {if (b&1){res*=a;res%=MOD;}b/=2;a*=a;a%=MOD;}return res;}
template<typename T> T powmod(T a, T b,T m) {T res=1;while (b>0) {if (b&1){res*=a;res%=m;}b/=2;a*=a;a%=m;}return res%m;}
template<typename T> T nlcm(const vector<T> &a) {T res;res = a[0];for (ll i = 1; i < (ll)a.size(); i++) {res = lcm(res, a[i]);}return res;}
template<typename T> T ngcd(const vector<T> &a){T res;res = a[0];for(ll i = 1; i < (ll)a.size() && res != 1; i++) {res = gcd(a[i], res);}return res;}
template<typename T> T sqr(T x){T r=sqrt(x)-1;while((r+1)*(r+1)<=x)r++;return r;}
template<typename T> T bit_length(T a){T k = 0;while(a){k++;a/=2;}return k;}
template<typename T> T isqrt(T n){T a = 0, r = 0;for(T s = bit_length(n)-(bit_length(n)%2?1:2); s >= 0;s-=2){T t = ((n >> s) & 3);r = ((r << 2) | t);T c = ((a << 2) | 1);int b = (r >= c);if(b){r -= c;}a = ((a << 1) | b);}return a;}
int popcount(long long a){return __builtin_popcountll(a);}
int popcount(int a){return __builtin_popcount(a);}
template<typename T> T ceil(T a, T b) {if(b < 0) a = -a, b = -b;return (a >= 0 ? (a + b - 1) / b : a / b);}
template<typename T> T floor(T a, T b) {if(b < 0) a = -a, b = -b;return (a >= 0 ? a / b : (a - b + 1) / b);}
template<typename T> T sum_of_digit(T a) {T res = 0;while(a){res += a%10; a /= 10;}return res;}
template<typename T ,typename A> void add_edge(vector<vector<T>> &G, A a, A b,bool directed = false){G[a].emplace_back(b);if(!directed)G[b].emplace_back(a);}
template<typename T ,typename A> void add_edge(vector<vector<pair<T,T>>> &G, A a, A b, A p,bool directed = false){G[a].emplace_back(p,b);if(!directed)G[b].emplace_back(p,a);}
#ifdef __HOGE__
#pragma endregion
#endif

//#include<atcoder/all>
//using namespace atcoder;

/* 二重辺連結成分分解 O(V+E)
二辺連結成分分解とも. 二重辺連結成分とは, 1本の辺を取り除いても連結である部分グラフである. 
つまり, 橋を含まない部分グラフなので, 橋を列挙することで二重辺連結成分を列挙できる.
二重辺連結成分で縮約後の頂点と橋からなるグラフは森になっている.

build(): 二重辺連結成分分解する. 
tree には縮約後の頂点からなる森が格納される. 
comp には各頂点が属する二重辺連結成分の頂点番号が格納される. 
group には各二重辺連結成分について, それに属する頂点が格納される.
*/
template< typename T>
struct TwoEdgeConnectedComponents {
public:
  std::vector<int> order, low, articulation,odd;
  std::vector<std::pair<int, int>> bridge;
  std::vector<vector<T>> G;
  vector< int > comp;
  vector<vector<T>> tree;
  vector< vector< int > > group;

  int operator[](const int &k) const {
    return comp[k];
  }

  void build(){
    int n = G.size();
    order.resize(n, -1);
    low.resize(n);
    odd.resize(n,0);
    order_next = 0;
    for(int i = 0; i < n; i++)
        if(order[i] == -1) dfs_lowlink(i);

    comp.assign(G.size(), -1);
    int k = 0;
    for(int i = 0; i < (int) comp.size(); i++) {
      if(comp[i] == -1) dfs(i, -1, k);
    }
    group.resize(k);
    for(int i = 0; i < (int) G.size(); i++) {
      group[comp[i]].emplace_back(i);
    }
    tree.resize(k);
    for(auto &e : bridge) {
      tree[comp[e.first]].emplace_back(comp[e.second]);
      tree[comp[e.second]].emplace_back(comp[e.first]);
    }
  }

  TwoEdgeConnectedComponents(const vector<vector< T >> &g) : G(g) {build();}

private:
  void dfs(int idx, int par, int &k) {
    if(par >= 0 && order[par] >= low[idx]) comp[idx] = comp[par];
    else comp[idx] = k++;
    for(auto &to : G[idx]) {
      if(comp[to] == -1) dfs(to, idx, k);
    }
  }
  int order_next;
   void dfs_lowlink(int now, int par = -1) {
       low[now] = order[now] = order_next++;
       bool is_articulation = false;
       int cnt = 0, cnt_par = 0;
       for(const auto &ed : G[now]) {
           const int &nxt = ed;
           if(order[nxt] == -1) {
               cnt++;
               int cur = order_next;
               dfs_lowlink(nxt, now);
               if(order[now] < low[nxt]) bridge.push_back(std::minmax(now, nxt));
               if(order[now] <= low[nxt]) is_articulation = true;
               if(order[now] <= low[nxt] && (order_next - cur)%2)odd[now] = 1;
               low[now] = std::min(low[now], low[nxt]);
           } else if(nxt != par or cnt_par++ == 1) {
               low[now] = std::min(low[now], order[nxt]);
           }
       }
       if(par == -1 and cnt < 2) is_articulation = false;
       if(is_articulation) articulation.push_back(now);
       return;
   }
};

//segmenttree
//findや、applyは半開区間
//要素にも作用素にも非可換モノイドが使用可

template <typename U>
class segment_tree{

    using T = typename U::typeT;
    using E = typename U::typeE;
    int num = 0, lognum = 0;
    std::vector<T> segtree_t;
    std::vector<E> segtree_e;
    std::vector<int> width;

public:

    segment_tree(int n, T deft){
        _constructor(n);
        std::fill(segtree_t.begin() + (1 << lognum), segtree_t.begin() + (1 << lognum) + n, deft);
        if(U::segtree_type != 2) for(int i = (1 << lognum) - 1; i != 0; i--){
            segtree_t[i] = U::func_tt(segtree_t[i << 1], segtree_t[(i << 1) + 1]);
        }
    }

    segment_tree(std::vector<T> &vec){
        _constructor(vec.size());
        std::copy(vec.begin(), vec.end(), segtree_t.begin() + (1 << lognum));
        if(U::segtree_type != 2) for(int i = (1 << lognum) - 1; i != 0; i--){
            segtree_t[i] = U::func_tt(segtree_t[i << 1], segtree_t[(i << 1) + 1]);
        }
    }

    void _constructor(int n){
        num = n;
        while((1 << lognum) < n) lognum++;
        segtree_t = std::vector<T>(1 << (lognum + 1), U::e_t);

        if(U::segtree_type != 1){
            segtree_e = std::vector<E>(1 << (lognum + 1), U::e_e);
        }
        if(U::segtree_type == 3){
            width = std::vector<int>(1 << (lognum + 1), 1);
            for(int i = (1 << lognum) - 1; i != 0; i--){
                width[i] = width[i << 1] + width[(i << 1) + 1];
            }
        }
    }

    inline void split_query(int ind){
        int ind2 = (ind << 1);
        if(U::segtree_type == 3){
            segtree_t[ind2]     = U::func_te(segtree_t[ind2]    , segtree_e[ind], width[ind2]);
            segtree_t[ind2 + 1] = U::func_te(segtree_t[ind2 + 1], segtree_e[ind], width[ind2]);
        }
        if(U::segtree_type != 1){
            segtree_e[ind2]     = U::func_ee(segtree_e[ind2]    , segtree_e[ind]);
            segtree_e[ind2 + 1] = U::func_ee(segtree_e[ind2 + 1], segtree_e[ind]);
            segtree_e[ind] = U::e_e;
        }
    }

    void apply(int bg, int ed, E query){
        if(U::segtree_type != 1){
            bg += (1 << lognum);
            ed += (1 << lognum);

            for(int i = lognum; i >= 1; i--){
                if(((bg >> i) << i) != bg) split_query(bg >> i);
                if(((ed >> i) << i) != ed) split_query((ed - 1) >> i);
            }

            int bg_temp = bg, ed_temp = ed - 1;
            while(bg_temp < ed_temp){
                if(bg_temp & 1){
                    segtree_e[bg_temp] = U::func_ee(segtree_e[bg_temp], query);
                    if(U::segtree_type == 3) segtree_t[bg_temp] = U::func_te(segtree_t[bg_temp], query, width[bg_temp]);
                    bg_temp++;
                }
                if(~ed_temp & 1){
                    segtree_e[ed_temp] = U::func_ee(segtree_e[ed_temp], query);
                    if(U::segtree_type == 3) segtree_t[ed_temp] = U::func_te(segtree_t[ed_temp], query, width[ed_temp]);
                    ed_temp--;
                }
                bg_temp >>= 1;
                ed_temp >>= 1;
            }
            if(bg_temp == ed_temp){
                segtree_e[bg_temp] = U::func_ee(segtree_e[bg_temp], query);
                if(U::segtree_type == 3) segtree_t[bg_temp] = U::func_te(segtree_t[bg_temp], query, width[bg_temp]);
            }

            if(U::segtree_type == 3) for(int i = 1; i <= lognum; i++){
                if(((bg >> i) << i) != bg){
                    segtree_t[bg >> i] = U::func_tt(segtree_t[(bg >> i) << 1], segtree_t[((bg >> i) << 1) + 1]);
                }
                if(((ed >> i) << i) != ed){
                    segtree_t[(ed - 1) >> i] = U::func_tt(segtree_t[((ed - 1) >> i) << 1], segtree_t[(((ed - 1) >> i) << 1) + 1]);
                }
            }
        }
    }

    void apply(int ind, E query){
        if(U::segtree_type == 1){
            ind += (1 << lognum);
            segtree_t[ind] = U::func_te(segtree_t[ind], query, 1);
            ind >>= 1;
            for(; ind != 0; ind >>= 1){
                segtree_t[ind] = U::func_tt(segtree_t[ind << 1], segtree_t[(ind << 1) + 1]);
            }
        }
    }

    T find(int bg, int ed){
        if(U::segtree_type != 2){
            bg += (1 << lognum);
            ed += (1 << lognum);
            
            if(U::segtree_type == 3) for(int i = lognum; i >= 1; i--){
                if(((bg >> i) << i) != bg) split_query(bg >> i);
                if(((ed >> i) << i) != ed) split_query((ed - 1) >> i);
            }

            T res1 = U::e_t, res2 = U::e_t;
            ed--;
            while(bg < ed){
                if(bg & 1){
                    res1 = U::func_tt(res1, segtree_t[bg]);
                    bg++;
                }
                if(~ed & 1){
                    res2 = U::func_tt(segtree_t[ed], res2);
                    ed--;
                }
                bg >>= 1;
                ed >>= 1;
            }
            if(bg == ed) res1 = U::func_tt(res1, segtree_t[bg]);
            res1 = U::func_tt(res1, res2);
            return res1;
        }
        return U::e_t;
    }

    T find(int ind){
        if(U::segtree_type == 2){
            ind += (1 << lognum);
            for(int i = lognum; i >= 1; i--){
                split_query(ind >> i);
            }

            segtree_t[ind] = U::func_te(segtree_t[ind], segtree_e[ind], 1);
            segtree_e[ind] = U::e_e;
            return segtree_t[ind];
        }
        return U::e_t;
    }

    void print(int n){
        std::cout << "val : ";
        for(auto itr = segtree_t.begin(); itr != segtree_t.end(); itr++){
            std::cout << std::right << std::setw(n) << *itr << " ";
        }
        std::cout << "\n";
        std::cout << "lazy: ";
        for(auto itr = segtree_e.begin(); itr != segtree_e.end(); itr++){
            std::cout << std::right << std::setw(n) << *itr << " ";
        }
        std::cout << "\n";
    }
};
//segment_tree<QUERY<ll>> Seg(vector）　で宣言
/*
template <typename T>
struct FINDquery_APPLYquery{
    static constexpr int segtree_type = 1:一点更新区間取得  2:区間更新一点取得  3:区間更新区間取得;
    using typeT = T;
    using typeE = T;
    static constexpr typeT e_t = 要素モノイドの単位元;（type2の時不要）
    static constexpr typeT e_e = 作用素モノイドの単位元;（type1の時不要）
    static typeT func_tt(typeT a, typeT b){return 要素モノイド同士の演算;}（type2の時不要）
    static typeT func_te(typeT a, typeE b, int w){return 作用素モノイドの要素モノイドへの作用;}
    static typeE func_ee(typeE a, typeE b){return 作用素モノイド同士の演算;}(type1の時不要）)
};
*/

template <typename G> struct HLDecomposition {
    G &g;
    vector<int> sz, in, out, head, rev, par, d;
 
    HLDecomposition(G &g) : g(g), d(g.size()), sz(g.size()), in(g.size()), out(g.size()), head(g.size()), rev(g.size()), par(g.size()) {}
 
    void dfs_sz(int idx, int p) {
        par[idx] = p;
        sz[idx] = 1;
        if(g[idx].size() and g[idx][0] == p) swap(g[idx][0], g[idx].back());
        for(auto &to : g[idx]) {
            if(to == p) continue;
            d[to] = d[idx] + 1;
            dfs_sz(to, idx);
            sz[idx] += sz[to];
            if(sz[g[idx][0]] < sz[to]) swap(g[idx][0], to);
        }
    }
 
    void dfs_hld(int idx, int par, int &times) {
        in[idx] = times++;
        rev[in[idx]] = idx;
        for(auto &to : g[idx]) {
            if(to == par) continue;
            head[to] = (g[idx][0] == to ? head[idx] : to);
            dfs_hld(to, idx, times);
        }
        out[idx] = times;
    }
 
    template <typename T> void dfs_hld(int idx, int par, int &times, vector<T> &v) {
        in[idx] = times++;
        rev[in[idx]] = idx;
        for(auto &to : g[idx]) {
            if(to == par) {
                v[in[idx]] = to.cost;
                continue;
            }
            head[to] = (g[idx][0] == to ? head[idx] : to);
            dfs_hld(to, idx, times, v);
        }
        out[idx] = times;
    }
 
    template <typename T> void dfs_hld(int idx, int par, int &times, vector<T> &v, vector<T> &a) {
        in[idx] = times++;
        rev[in[idx]] = idx;
        v[in[idx]] = a[idx];
        for(auto &to : g[idx]) {
            if(to == par) continue;
            head[to] = (g[idx][0] == to ? head[idx] : to);
            dfs_hld(to, idx, times, v, a);
        }
        out[idx] = times;
    }
 
    void build(int root = 0) {
        head[root] = root;
        dfs_sz(root, -1);
        int t = 0;
        dfs_hld(root, -1, t);
    }
 
    template <typename T> vector<T> build(int root = 0) {
        head[root] = root;
        dfs_sz(root, -1);
        int t = 0;
        vector<T> res(g.size());
        dfs_hld(root, -1, t, res);
        return res;
    }
 
    template <typename T> vector<T> build(vector<T> &a, int root = 0) {
        head[root] = root;
        dfs_sz(root, -1);
        int t = 0;
        vector<T> res(g.size());
        dfs_hld(root, -1, t, res, a);
        return res;
    }
 
    int la(int v, int k) {
        while(1) {
            int u = head[v];
            if(in[v] - k >= in[u]) return rev[in[v] - k];
            k -= in[v] - in[u] + 1;
            v = par[u];
        }
    }
 
    int lca(int u, int v) {
        for(;; v = par[head[v]]) {
            if(in[u] > in[v]) swap(u, v);
            if(head[u] == head[v]) return u;
        }
    }
 
    template <typename T, typename Q, typename F> T query(int u, int v, const T &e, const Q &q, const F &f, bool edge = false) {
        T l = e, r = e;
        for(;; v = par[head[v]]) {
            if(in[u] > in[v]) swap(u, v), swap(l, r);
            if(head[u] == head[v]) break;
            l = f(q(in[head[v]], in[v] + 1), l);
        }
        return f(f(q(in[u] + edge, in[v] + 1), l), r);
    }
    
 
    template <typename T, typename Q, typename Q2, typename F> T query(int u, int v, const T &e, const Q &q1, const Q2 &q2, const F &f, bool edge = false) {
        T l = e, r = e;
        for(;;) {
            if(head[u] == head[v]) break;
            if(in[u] > in[v]) {
                l = f(l, q2(in[head[u]], in[u] + 1));
                u = par[head[u]];
            } else {
                r = f(q1(in[head[v]], in[v] + 1), r);
                v = par[head[v]];
            }
        }
        if(in[u] > in[v]) return f(f(l, q2(in[v] + edge, in[u] + 1)), r);
        return f(f(l, q1(in[u] + edge, in[v] + 1)), r);
    }

    //query [u, v], q([left, right])
    template <typename Q> void add(int u, int v, const Q &q, bool edge = false) {
        if(edge){
            while (true) {
                if (in[u] > in[v]) swap(u, v);
                if (head[u] != head[v]) {
                    q(in[head[v]], in[v]);
                    v = par[head[v]];
                }
                else {
                    if (u != v) q(in[u] + 1, in[v]);
                    break;
                }
            }
        }else{
            while (true) {
                if (in[u] > in[v]) swap(u, v);
                q(max(in[head[v]], in[u]), in[v]);
                if (head[u] != head[v]) v = par[head[v]];
                else break;
            }
        }
    }
 
    constexpr int operator[](int k) { return in[k]; }
 
    int dist(int u, int v) { return d[u] + d[v] - 2 * d[lca(u, v)]; }
 
    // u -> v の unique path
    vector<int> road(int u, int v) {
        int l = lca(u, v);
        vector<int> a, b;
        for(; v != l; v = la(v)) b.emplace_back(v);
        for(; u != l; u = la(u)) a.emplace_back(u);
        a.emplace_back(l);
        for(int i = b.size() - 1; i >= 0; i--) a.emplace_back(b[i]);
        return a;
    }

    pair<int, int> subtree(int v, bool edge = false) { return pair<int, int>(in[v] + edge, out[v]); }
};

template <typename T>
struct RmaxQ_SUQ{
    static constexpr int segtree_type = 1;
    using typeT = pair<T,T>;
    using typeE = pair<T,T>;
    static constexpr typeT e_t = {-1,-1};
    static constexpr typeT e_e = {0,0};
    static typeT func_tt(typeT a, typeT b){return (a.first>b.first?a:b);}
    static typeT func_te(typeT a, typeE b, int w){return b;}
    static typeE func_ee(typeE a, typeE b){return {-1,-1};}
};

signed main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    //cout << fixed << setprecision(15);

    ll N,M,Q;
    cin >> N >> M >> Q;

    vvll G(N);
    rep(i,M){
      ll a,b;
      cin>> a >> b;
      a--; b--;
      add_edge(G,a,b);
    }

    TwoEdgeConnectedComponents<ll> tcc(G);

    auto tree = tcc.tree;
    int C = tree.size();

    HLDecomposition HLD(tree);
    HLD.build();
    vector<priority_queue<ll>> Values(C);
    vpll A(C);
    rep(i,C){
      A[i] = {-1,i};
    }
    segment_tree<RmaxQ_SUQ<ll>> Seg(A);


    while(Q--){
      ll t;
      cin >> t;
      if(t==1){
        ll U,W;
        cin >> U >> W;
        U--;
        U = tcc[U];
        Values[U].emplace(W);
        Seg.apply(HLD.in[U],{Values[U].top(),U});
      }else{
        ll S,T;
        cin >> S >> T;
        S--;T--;
        S = tcc[S];
        T = tcc[T];
        auto ans = HLD.query(S,T,RmaxQ_SUQ<ll>::e_t,[&](int a, int b) { return Seg.find(a, b); }, [&](pll a,pll b){return (a.first>b.first?a:b);},false);
        ll u = ans.second;
        if(u!=-1&&Values[u].size()){
          Values[u].pop();
          ll nn = -1;
          if(Values[u].size()) nn = Values[u].top();
          Seg.apply(HLD.in[u],{nn,u});
        }
        cout << ans.first << endl;
      }
    }





    //cout << ans << endl;

  return 0;
}