//#pragma GCC optimize ("-O3")
#include <bits/stdc++.h>
using namespace std;
//@起動時
struct initon {
    initon() {
        cin.tie(0);
        ios::sync_with_stdio(false);
        cout.setf(ios::fixed);
        cout.precision(16);
        srand((unsigned) clock() + (unsigned) time(NULL));
    };
} __initon;
//衝突対策
#define ws ___ws
struct T {
    int f, s, t;
    T() { f = -1, s = -1, t = -1; }
    T(int f, int s, int t) : f(f), s(s), t(t) {}
    bool operator<(const T &r) const {
        return f != r.f ? f < r.f : s != r.s ? s < r.s : t < r.t;
        //return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 大きい順
    }
    bool operator>(const T &r) const {
        return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t;
        //return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 小さい順
    }
    bool operator==(const T &r) const {
        return f == r.f && s == r.s && t == r.t;
    }
    bool operator!=(const T &r) const {
        return f != r.f || s != r.s || t != r.t;
    }
    int operator[](int i) {
        assert(i < 3);
        return i == 0 ? f : i == 1 ? s : t;
    }
};
#define int long long
#define ll long long
#define double long double
#define ull unsigned long long
using dou = double;
using itn = int;
using str = string;
using bo= bool;
#define au auto
using P = pair<ll, ll>;

#define fi first
#define se second
#define vec vector
#define beg begin
#define rbeg rbegin
#define con continue
#define bre break
#define brk break
#define is ==


//マクロ省略系 コンテナ

using vi = vector<int>;
#define _overloadvvi(_1, _2, _3, _4, name, ...) name
#define vvi0() vec<vi>
#define vvi1(a) vec<vi> a
#define vvi2(a, b) vec<vi> a(b)
#define vvi3(a, b, c) vec<vi> a(b,vi(c))
#define vvi4(a, b, c, d) vec<vi> a(b,vi(c,d))
#define vvi(...) _overloadvvi(__VA_ARGS__,vvi4,vvi3,vvi2 ,vvi1,vvi0)(__VA_ARGS__)


using vl = vector<ll>;
#define _overloadvvl(_1, _2, _3, _4, name, ...) name
#define vvl1(a) vec<vl> a
#define vvl2(a, b) vec<vl> a(b)
#define vvl3(a, b, c) vec<vl> a(b,vl(c))
#define vvl4(a, b, c, d) vec<vl> a(b,vl(c,d))
#define vvl(...) _overloadvvl(__VA_ARGS__,vvl4,vvl3,vvl2 ,vvl1)(__VA_ARGS__)

using vb = vector<bool>;
#define _overloadvvb(_1, _2, _3, _4, name, ...) name
#define vvb1(a) vec<vb> a
#define vvb2(a, b) vec<vb> a(b)
#define vvb3(a, b, c) vec<vb> a(b,vb(c))
#define vvb4(a, b, c, d) vec<vb> a(b,vb(c,d))
#define vvb(...) _overloadvvb(__VA_ARGS__,vvb4,vvb3,vvb2 ,vvb1)(__VA_ARGS__)

using vs = vector<string>;
#define _overloadvvs(_1, _2, _3, _4, name, ...) name
#define vvs1(a) vec<vs> a
#define vvs2(a, b) vec<vs> a(b)
#define vvs3(a, b, c) vec<vs> a(b,vs(c))
#define vvs4(a, b, c, d) vec<vs> a(b,vs(c,d))
#define vvs(...) _overloadvvs(__VA_ARGS__,vvs4,vvs3,vvs2 ,vvs1)(__VA_ARGS__)

using vd = vector<double>;
#define _overloadvvd(_1, _2, _3, _4, name, ...) name
#define vvd1(a) vec<vd> a
#define vvd2(a, b) vec<vd> a(b)
#define vvd3(a, b, c) vec<vd> a(b,vd(c))
#define vvd4(a, b, c, d) vec<vd> a(b,vd(c,d))
#define vvd(...) _overloadvvd(__VA_ARGS__,vvd4,vvd3,vvd2 ,vvd1)(__VA_ARGS__)

using vc=vector<char>;
#define _overloadvvc(_1, _2, _3, _4, name, ...) name
#define vvc1(a) vec<vc> a
#define vvc2(a, b) vec<vc> a(b)
#define vvc3(a, b, c) vec<vc> a(b,vc(c))
#define vvc4(a, b, c, d) vec<vc> a(b,vc(c,d))
#define vvc(...) _overloadvvc(__VA_ARGS__,vvc4,vvc3,vvc2 ,vvc1)(__VA_ARGS__)

using vp = vector<P>;
#define _overloadvvp(_1, _2, _3, _4, name, ...) name
#define vvp1(a) vec<vp> a
#define vvp2(a, b) vec<vp> a(b)
#define vvp3(a, b, c) vec<vp> a(b,vp(c))
#define vvp4(a, b, c, d) vec<vp> a(b,vp(c,d))

using vt = vector<T>;
#define _overloadvvt(_1, _2, _3, _4, name, ...) name
#define vvt1(a) vec<vt> a
#define vvt2(a, b) vec<vt> a(b)
#define vvt3(a, b, c) vec<vt> a(b,vt(c))
#define vvt4(a, b, c, d) vec<vt> a(b,vt(c,d))

#define v3i(a, b, c, d) vector<vector<vi>> a(b, vector<vi>(c, vi(d)))
#define v3d(a, b, c, d) vector<vector<vd>> a(b, vector<vd>(c, vd(d)))
#define v3m(a, b, c, d) vector<vector<vm>> a(b, vector<vm>(c, vm(d)))

#define _vvi vector<vi>
#define _vvl vector<vl>
#define _vvb vector<vb>
#define _vvs vector<vs>
#define _vvd vector<vd>
#define _vvc vector<vc>
#define _vvp vector<vp>

#define PQ priority_queue<ll, vector<ll>, greater<ll> >
#define tos to_string
using mapi = map<int, int>;
using mapd = map<dou, int>;
using mapc = map<char, int>;
using maps = map<str, int>;
using seti = set<int>;
using setd = set<dou>;
using setc = set<char>;
using sets = set<str>;
using qui = queue<int>;
#define bset bitset
#define uset unordered_set
#define mset multiset
#define umap unordered_map
#define umapi unordered_map<int,int>
#define umapp unordered_map<P,int>
#define mmap multimap

//マクロ 繰り返し
#define _overloadrep(_1, _2, _3, _4, name, ...) name
# define _rep(i, n) for(int i = 0,_lim=n; i < _lim ; i++)
#define repi(i, m, n) for(int i = m,_lim=n; i < _lim ; i++)
#define repadd(i, m, n, ad) for(int i = m,_lim=n; i < _lim ; i+= ad)
#define rep(...) _overloadrep(__VA_ARGS__,repadd,repi,_rep,)(__VA_ARGS__)
#define _rer(i, n) for(int i = n; i >= 0 ; i--)
#define reri(i, m, n) for(int i = m,_lim=n; i >= _lim ; i--)
#define rerdec(i, m, n, dec) for(int i = m,_lim=n; i >= _lim ; i-=dec)
#define rer(...) _overloadrep(__VA_ARGS__,rerdec,reri,_rer,)(__VA_ARGS__)
#define fora(a, b) for(auto&& a : b)

//マクロ 定数
#define k3 1010
#define k4 10101
#define k5 101010
#define k6 1010101
#define k7 10101010
const int inf = (int) 1e9 + 100;
const ll linf = (ll) 1e18 + 100;
const double eps = 1e-9;
const double PI = 3.1415926535897932384626433832795029L;
ll ma = numeric_limits<ll>::min();
ll mi = numeric_limits<ll>::max();
const int y4[] = {-1, 1, 0, 0};
const int x4[] = {0, 0, -1, 1};
const int y8[] = {0, 1, 0, -1, -1, 1, 1, -1};
const int x8[] = {1, 0, -1, 0, 1, -1, 1, -1};

//マクロ省略形 関数等
#define arsz(a) (sizeof(a)/sizeof(a[0]))
#define sz(a) ((int)(a).size())
#define rs resize
#define mp make_pair
#define pb push_back
#define pf push_front
#define eb emplace_back
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()


inline void sort(string &a) { sort(a.begin(), a.end()); }
template<class T> inline void sort(vector<T> &a) { sort(a.begin(), a.end()); };
template<class T> inline void sort(vector<T> &a, int len) { sort(a.begin(), a.begin() + len); };
template<class T, class F> inline void sort(vector<T> &a, F f) { sort(a.begin(), a.end(), [&](T l, T r) { return f(l) < f(r); }); };
enum ___pcomparator {
    fisi, fisd, fdsi, fdsd, sifi, sifd, sdfi, sdfd
};
inline void sort(vector<P> &a, ___pcomparator type) {
    switch (type) {
        case fisi:
            sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi < r.fi : l.se < r.se; });
            break;
        case fisd:
            sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi < r.fi : l.se > r.se; });
            break;
        case fdsi:
            sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi > r.fi : l.se < r.se; });
            break;
        case fdsd:
            sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi > r.fi : l.se > r.se; });
            break;
        case sifi:
            sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se < r.se : l.fi < r.fi; });
            break;
        case sifd:
            sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se < r.se : l.fi > r.fi; });
            break;
        case sdfi:
            sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se > r.se : l.fi < r.fi; });
            break;
        case sdfd:
            sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se > r.se : l.fi > r.fi; });
            break;
    }
};
inline void sort(vector<T> &a, ___pcomparator type) {
    switch (type) {
        case fisi:
            sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f < r.f : l.s < r.s; });
            break;
        case
            fisd:
            sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f < r.f : l.s > r.s; });
            break;
        case
            fdsi:
            sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f > r.f : l.s < r.s; });
            break;
        case
            fdsd:
            sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f > r.f : l.s > r.s; });
            break;
        case
            sifi:
            sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s < r.s : l.f < r.f; });
            break;
        case
            sifd:
            sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s < r.s : l.f > r.f; });
            break;
        case
            sdfi:
            sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s > r.s : l.f < r.f; });
            break;
        case
            sdfd:
            sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s > r.s : l.f > r.f; });
            break;
    }
};
template<class T> inline void rsort(vector<T> &a) { sort(a.begin(), a.end(), greater<T>()); };
template<class T> inline void rsort(vector<T> &a, int len) { sort(a.begin(), a.begin() + len, greater<T>()); };
template<class U, class F> inline void rsort(vector<U> &a, F f) { sort(a.begin(), a.end(), [&](U l, U r) { return f(l) > f(r); }); };
template<class U> inline void sortp(vector<U> &a, vector<U> &b) {
    vp c;
    int n = sz(a);
    assert(n == sz(b));
    rep(i, n)c.eb(a[i], b[i]);
    sort(c);
    rep(i, n) {
        a[i] = c[i].first;
        b[i] = c[i].second;;
    }
};
//F = T<T>
//例えばreturn p.fi + p.se;
template<class U, class F> inline void sortp(vector<U> &a, vector<U> &b, F f) {
    vp c;
    int n = sz(a);
    assert(n == sz(b));
    rep(i, n)c.eb(a[i], b[i]);
    sort(c, f);
    rep(i, n) {
        a[i] = c[i].first;
        b[i] = c[i].second;
    }
};
template<class U, class F> inline void sortp(vector<U> &a, vector<U> &b, char type) {
    vp c;
    int n = sz(a);
    assert(n == sz(b));
    rep(i, n)c.eb(a[i], b[i]);
    sort(c, type);
    rep(i, n) {
        a[i] = c[i].first;
        b[i] = c[i].second;
    }
};
template<class U> inline void rsortp(vector<U> &a, vector<U> &b) {
    vp c;
    int n = sz(a);
    assert(n == sz(b));
    rep(i, n)c.eb(a[i], b[i]);
    rsort(c);
    rep(i, n) {
        a[i] = c[i].first;
        b[i] = c[i].second;
    }
};
template<class U, class F> inline void rsortp(vector<U> &a, vector<U> &b, F f) {
    vp c;
    int n = sz(a);
    assert(n == sz(b));
    rep(i, n)c.eb(a[i], b[i]);
    rsort(c, f);
    rep(i, n) {
        a[i] = c[i].first;
        b[i] = c[i].second;
    }
};
template<class U> inline void sortt(vector<U> &a, vector<U> &b, vector<U> &c) {
    vt r;
    int n = sz(a);
    assert(n == sz(b));
    assert(n == sz(c));
    rep(i, n)r.eb(a[i], b[i], c[i]);
    sort(r);
    rep(i, n) {
        a[i] = r[i].f;
        b[i] = r[i].s;
        c[i] = r[i].t;
    }
};
template<class U, class F> inline void sortt(vector<U> &a, vector<U> &b, vector<U> &c, F f) {
    vt r;
    int n = sz(a);
    assert(n == sz(b));
    assert(n == sz(c));
    rep(i, n)r.eb(a[i], b[i], c[i]);
    sort(r, f);
    rep(i, n) {
        a[i] = r[i].f;
        b[i] = r[i].s;
        c[i] = r[i].t;
    }
};
template<class U, class F> inline void rsortt(vector<U> &a, vector<U> &b, vector<U> &c, F f) {
    vt r;
    int n = sz(a);
    assert(n == sz(b));
    assert(n == sz(c));
    rep(i, n)r.eb(a[i], b[i], c[i]);
    rsort(r, f);
    rep(i, n) {
        a[i] = r[i].f;
        b[i] = r[i].s;
        c[i] = r[i].t;
    }
};
template<class T> inline void sort2(vector<vector<T>> &a) { for (int i = 0, n = a.size(); i < n; i++)sort(a[i]); }
template<class T> inline void rsort2(vector<vector<T>> &a) { for (int i = 0, n = a.size(); i < n; i++)rsort(a[i]); }
template<typename A, size_t N, typename T> void fill(A (&a)[N], const T &v) { rep(i, N)a[i] = v; }
template<typename A, size_t N, size_t O, typename T> void fill(A (&a)[N][O], const T &v) { rep(i, N)rep(j, O)a[i][j] = v; }
template<typename A, size_t N, size_t O, size_t P, typename T> void fill(A (&a)[N][O][P], const T &v) { rep(i, N)rep(j, O)rep(k, P)a[i][j][k] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, typename T> void fill(A (&a)[N][O][P][Q], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)a[i][j][k][l] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, typename T> void fill(A (&a)[N][O][P][Q][R], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)a[i][j][k][l][m] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, size_t S, typename T> void fill(A (&a)[N][O][P][Q][R][S], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)rep(n, S)a[i][j][k][l][m][n] = v; }

template<typename V, typename T>
void fill(V &xx, const T vall) {
    xx = vall;
}
template<typename V, typename T>
void fill(vector<V> &vecc, const T vall) {
    for (auto &&vx: vecc) fill(vx, vall);
}

//@汎用便利関数 入力
template<typename T = int> T _in() {
    T x;
    cin >> x;
    return (x);
}
#define _overloadin(_1, _2, _3, _4, name, ...) name
#define in0() _in()
#define in1(a) cin>>a
#define in2(a, b) cin>>a>>b
#define in3(a, b, c) cin>>a>>b>>c
#define in4(a, b, c, d) cin>>a>>b>>c>>d
#define in(...) _overloadin(__VA_ARGS__,in4,in3,in2 ,in1,in0)(__VA_ARGS__)

#define _overloaddin(_1, _2, _3, _4, name, ...) name
#define din1(a) int a;cin>>a
#define din2(a, b) int a,b;cin>>a>>b
#define din3(a, b, c) int a,b,c;cin>>a>>b>>c
#define din4(a, b, c, d) int a,b,c,d;cin>>a>>b>>c>>d
#define din(...) _overloadin(__VA_ARGS__,din4,din3,din2 ,din1)(__VA_ARGS__)

#define _overloaddind(_1, _2, _3, _4, name, ...) name
#define din1d(a) int a;cin>>a;a--
#define din2d(a, b) int a,b;cin>>a>>b;a--,b--
#define din3d(a, b, c) int a,b,c;cin>>a>>b>>c;a--,b--,c--
#define din4d(a, b, c, d) int a,b,c,d;cin>>a>>b>>c>>d;;a--,b--,c--,d--
#define dind(...) _overloaddind(__VA_ARGS__,din4d,din3d,din2d ,din1d)(__VA_ARGS__)


string sin() { return _in<string>(); }
ll lin() { return _in<ll>(); }
#define na(a, n) a.resize(n); rep(i,n) cin >> a[i];
#define nao(a, n) a.resize(n+1); rep(i,n) cin >> a[i+1];
#define nad(a, n) a.resize(n); rep(i,n){ cin >> a[i]; a[i]--;}
#define na2(a, b, n) a.resize(n),b.resize(n);rep(i, n)cin >> a[i] >> b[i];
#define na2d(a, b, n) a.resize(n),b.resize(n);rep(i, n){cin >> a[i] >> b[i];a[i]--,b[i]--;}
#define na3(a, b, c, n) a.resize(n),b.resize(n),c.resize(n);   rep(i, n)cin >> a[i] >> b[i] >> c[i];
#define na3d(a, b, c, n) a.resize(n),b.resize(n),c.resize(n);   rep(i, n){cin >> a[i] >> b[i] >> c[i];a[i]--,b[i]--,c[i]--;}
#define nt(a, h, w) resize(a,h,w);rep(hi,h)rep(wi,w) cin >> a[hi][wi];
#define ntd(a, h, w) rs(a,h,w);rep(hi,h)rep(wi,w) cin >> a[hi][wi], a[hi][wi]--;
#define ntp(a, h, w) fill(a,'#');rep(hi,1,h+1)rep(wi,1,w+1) cin >> a[hi][wi];

//デバッグ
#define sp << " " <<

#define debugName(VariableName) # VariableName

#define _deb1(x) cerr <<  debugName(x)<<" = "<<x << endl
#define _deb2(x, y) cerr <<  debugName(x)<<" = "<<x<<", "<< debugName(y)<<" = "<<y<< endl
#define _deb3(x, y, z) cerr <<  debugName(x)<<" = "<<x  << ", " <<  debugName(y)<<" = "<<y <<", " debugName(z)<<" = "<<z <<endl
#define _deb4(x, y, z, a) cerr <<  debugName(x)<<" = "<<x <<", " <<   debugName(y)<<" = "<<y <<", " <<  debugName(z)<<" = "<<z <<", " <<  debugName(a)<<" = "<<a<<endl
#define _deb5(x, y, z, a, b) cerr <<  debugName(x)<<" = "<<x <<", " <<   debugName(y)<<" = "<<y <<", " <<  debugName(z)<<" = "<<z <<", " <<  debugName(a)<<" = "<<a<<", " <<  debugName(b)<<" = "<<b<<endl


#define _overloadebug(_1, _2, _3, _4, _5, name, ...) name
#define debug(...) _overloadebug(__VA_ARGS__,_deb5,_deb4,_deb3,_deb2,_deb1)(__VA_ARGS__)
#define deb(...) _overloadebug(__VA_ARGS__,_deb5,_deb4,_deb3,_deb2,_deb1)(__VA_ARGS__)
#define debugline(x) cerr << x << " " << "(L:" << __LINE__ << ")" << '\n'
void ole() {
#ifdef _DEBUG
    debugline("ole");
    exit(0);
#endif
    string a = "a";
    rep(i, 30)a += a;
    rep(i, 1 << 17)cout << a << endl;
    cout << "OLE 出力長制限超過" << endl;
    exit(0);
}
void tle() { while (inf)cout << inf << endl; }
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll gcd(vi b) {
    ll res = b[0];
    for (auto &&v :b)res = gcd(v, res);
    return res;
}
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
ll rev(ll a) {
    ll res = 0;
    while (a) {
        res *= 10;
        res += a % 10;
        a /= 10;
    }
    return res;
}
template<class T> void rev(vector<T> &a) {
    reverse(all(a));
}
void rev(string &a) {
    reverse(all(a));
}
ll ceil(ll a, ll b) {
    if (b == 0) {
        debugline("ceil");
        deb(a, b);
        ole();
        return -1;
    } else return (a + b - 1) / b;
}
ll sqrt(ll a) {
    if (a < 0) {
        debugline("sqrt");
        deb(a);
        ole();
    }
    ll res = (ll) std::sqrt(a);
    while (res * res < a)res++;
    return res;
}
double log(double e, double x) { return log(x) / log(e); }
ll sig(ll t) { return (1 + t) * t / 2; }
ll sig(ll s, ll t) { return (s + t) * (t - s + 1) / 2; }

vi divisors(int v) {
    vi res;
    double lim = std::sqrt(v);
    for (int i = 1; i <= lim; ++i) {
        if (v % i == 0) {
            res.pb(i);
            if (i != v / i)res.pb(v / i);
        }
    }
    return res;
}

vb isPrime;
vi primes;

void setPrime() {
    int len = 4010101;
    isPrime.resize(4010101);
    fill(isPrime, true);
    isPrime[0] = isPrime[1] = false;
    for (int i = 2; i <= sqrt(len) + 5; ++i) {
        if (!isPrime[i])continue;
        for (int j = 2; i * j < len; ++j) {
            isPrime[i * j] = false;
        }
    }
    rep(i, len)if (isPrime[i])primes.pb(i);
}

vi factorization(int v) {
    int tv = v;
    vi res;
    if (isPrime.size() == 0)setPrime();
    for (auto &&p :primes) {
        if (v % p == 0)res.push_back(p);
        while (v % p == 0) {
            v /= p;
        }
        if (v == 1 || p * p > tv)break;
    }
    if (v > 1)res.pb(v);
    return res;
}
inline bool inside(int h, int w, int H, int W) { return h >= 0 && w >= 0 && h < H && w < W; }
inline bool inside(int v, int l, int r) { return l <= v && v < r; }
#define ins inside
ll u(ll a) { return a < 0 ? 0 : a; }
template<class T> vector<T> u(const vector<T> &a) {
    vector<T> ret = a;
    fora(v, ret)v = u(v);
    return ret;
}
#define MIN(a) numeric_limits<a>::min()
#define MAX(a) numeric_limits<a>::max()

void yn(bool a) {
    if (a)cout << "yes" << endl;
    else cout << "no" << endl;
}
void Yn(bool a) {
    if (a)cout << "Yes" << endl;
    else cout << "No" << endl;
}
void YN(bool a) {
    if (a)cout << "YES" << endl;
    else cout << "NO" << endl;
}
void fyn(bool a) {
    if (a)cout << "yes" << endl;
    else cout << "no" << endl;
    exit(0);
}
void fYn(bool a) {
    if (a)cout << "Yes" << endl;
    else cout << "No" << endl;
    exit(0);
}
void fYN(bool a) {
    if (a)cout << "YES" << endl;
    else cout << "NO" << endl;
    exit(0);
}
void Possible(bool a) {
    if (a)cout << "Possible" << endl;
    else cout << "Impossible" << endl;
    exit(0);
}
void POSSIBLE(bool a) {
    if (a)cout << "POSSIBLE" << endl;
    else cout << "IMPOSSIBLE" << endl;
    exit(0);
}
template<class T, class U> set<T> &operator+=(set<T> &a, U v) {
    a.insert(v);
    return a;
}
template<class T, class U> vector<T> &operator+=(vector<T> &a, U v) {
    a.pb(v);
    return a;
}
template<class T> T sum(vector<T> &v, int s = 0, int t = inf) {
    T ret = 0;
    rep(i, s, min(sz(v), t))ret += v[i];
    return ret;
}
void mod(int &a, int m) { a = (a % m + m) % m; }
template<class F> inline int mgr(int ok, int ng, F f) {
#define _mgrbody int mid = (ok + ng) / 2; if (f(mid))ok = mid; else ng = mid;
    if (ok < ng)while (ng - ok > 1) { _mgrbody } else while (ok - ng > 1) { _mgrbody }
    return ok;
}

template<class F> inline int mgr(int ok, int ng, int second, F f) {
#define _mgrbody2 int mid = (ok + ng) / 2; if (f(mid, second))ok = mid; else ng = mid;
    if (ok < ng) while (ng - ok > 1) { _mgrbody2 } else while (ok - ng > 1) { _mgrbody2 }
    return ok;
}
template<typename T> ostream &operator<<(ostream &os, vector<T> &m) {
    for (auto &&v:m) os << v << " ";
    return os;
}
constexpr bool bget(ll m, int keta) { return (m >> keta) & 1; }
int bget(ll m, int keta, int sinsuu) {
    m /= (ll) pow(sinsuu, keta);
    return m % sinsuu;
}
ll bit(int n) { return (1LL << (n)); }
ll bit(int n, int sinsuu) { return (ll) pow(sinsuu, n); }
int mask(int n) { return (1ll << n) - 1; }
#define bcou __builtin_popcountll
template<class T> vector<T> ruiv(vector<T> &a) {
    vector<T> ret(a.size() + 1);
    rep(i, a.size())ret[i + 1] = ret[i] + a[i];
    return ret;
}
template<class T, class U> inline bool chma(T &a, const U &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template<class U> inline bool chma(const U &b) { return chma(ma, b); }
template<class T, class U> inline bool chmi(T &a, const U &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}
template<class U> inline bool chmi(const U &b) { return chmi(mi, b); }
#define unique(v) v.erase( unique(v.begin(), v.end()), v.end() );

int n, m, k, d, H, W, x, y, z, q;
int cou;
vi a, b, c;
vvi (s, 0, 0);
vvc (ba, 0, 0);
vp p;

//@formatter:off
#define forg(gi, ve) for (ll gi = 0,forglim = ve.size(), f, t, c; gi < forglim && (f = ve[gi].f, t = ve[gi].t, c = ve[gi].c, true); ++gi)
#define fort(gi, ve) for (ll gi = 0, f, t, c; gi < ve.size() && (f = ve[gi].f, t = ve[gi].t, c = ve[gi].c, true); ++gi)if(t!=p)
//typeが追加される
#define forg2(gi, ve) for (ll gi = 0,forglim = ve.size(), f, t, c,ty; gi < forglim && (f = ve[gi].f, t = ve[gi].t, c = ve[gi].c,ty=ve[gi].ty, true); ++gi)
#define fort2(gi, ve) for (ll gi = 0, f, t, c,ty; gi < ve.size() && (f = ve[gi].f, t = ve[gi].t, c = ve[gi].c,ty=ve[gi].ty, true); ++gi)if(t!=p)
template<class T> struct edge { int f, t; T c; int id; int ty; edge(int f, int t, T c = 1,  int ty = -1,int id = -1) : f(f), t(t), c(c), id(id), ty(ty) {} bool operator<(const edge &b) const { return c < b.c; } bool operator>(const edge &b) const { return c > b.c; }};
template<class T> ostream &operator<<(ostream &os, edge<T> &e) {    os << e.f << " " << e.t << " " << e.c;    return os;}
template<typename T> class graph {protected:    vector<bool> usedv;public :    vector<vector<edge<T>>> g;    vector<edge<T>> edges;    int n;    graph(int n) : n(n) { g.resize(n), usedv.resize(n); }    void clear() { g.clear(), edges.clear(); }    void resize(int n) {        this->n = n;        g.resize(n);        usedv.resize(n);    }    int size() { return g.size(); }    vector<edge<T> > &operator[](int i) { return g[i]; }    virtual void add(int f, int t, T c, int ty ,int id) = 0;    virtual bool used(edge<T> &e) = 0;    virtual bool used(int id) = 0;    virtual void del(edge<T> &e) = 0;    virtual void del(int id) = 0;    virtual void set_edges() = 0;};
template<typename T =ll> class digraph : public graph<T> {
public:
    using graph<T>::g;
    using graph<T>::n;
    using graph<T>::edges;
    using graph<T>::usedv;
    int eid = 0;

    digraph(int n) : graph<T>(n) {}
    void add(int f, int t, T c = 1, int ty = -1,int id = -1) {
        if (!(0 <= f && f < n && 0 <= t && t < n)) {
            debugline("digraph add");
            deb(f, t, c, ty,id);
            ole();
        }
        if (id == -1)id = eid++;
        g[f].emplace_back(f, t, c, ty,id);
        edges.emplace_back(f, t, c, ty,id);
    }
    bool used(edge<T> &e) { return usedv[e.id]; }
    bool used(int id) { return usedv[id]; }
    void del(edge<T> &e) { usedv[e.id] = usedv[e.id ^ 1] = 1; }
    void del(int id) { usedv[id] = usedv[id ^ 1] = 1; }
    void set_edges() {        if (sz(edges))return;        rep(i, n)fora(e, g[i])edges.push_back(e);    }
};
template<class T=int> class undigraph : public graph<T> {
public:
    using graph<T>::g;
    using graph<T>::n;
    using graph<T>::edges;
    using graph<T>::usedv;
    int eid = 0;
    undigraph(int n) : graph<T>(n) {}
    void add(int f, int t, T c = 1,  int ty = -1,int id = -1) {
        if (!(0 <= f && f < n && 0 <= t && t < n)) {
            debugline("undigraph add");
            deb(f, t, c,  ty,id);
            ole();
        }
        if (id == -1)id = eid, eid += 2;
        g[f].emplace_back(f, t, c, ty, id);
        g[t].emplace_back(t, f, c, ty, id + 1);
        edges.emplace_back(f, t, c, ty, id);
        edges.emplace_back(t, f, c, ty, id + 1);
    }
    void add(edge<T> &e) {        int f = e.f, t = e.t, ty = e.ty;        T c = e.c;        add(f, t, c, ty);    }
    bool used(edge<T> &e) { return usedv[e.id]; }
    bool used(int id) { return usedv[id]; }
    void del(edge<T> &e) { usedv[e.id] = usedv[e.id ^ 1] = 1; }
    void del(int id) { usedv[id] = usedv[id ^ 1] = 1; }
    void set_edges() {        if (sz(edges))return;        rep(i, n)fora(e, g[i])edges.push_back(e);    }
};
template<typename T> struct LowLink { /*@formatter:off*/   undigraph<T> &g;    vector<int> used, ord, low;    vector<int> articulation;    vector<pair<int, int> > bridge;    LowLink(undigraph<T> &g) : g(g) {}    int dfs(int idx, int k, int par) {        used[idx] = true;        ord[idx] = k++;        low[idx] = ord[idx];        bool is_articulation = false;        int cnt = 0;        forg(gi, g[idx]) {            if (!used[t]) {                ++cnt;                k = dfs(t, k, idx);                low[idx] = min(low[idx], low[t]);                is_articulation |= ~par && low[t] >= ord[idx];                if (ord[idx] < low[t]) bridge.emplace_back(minmax(idx, (int) t));            } else if (t != par) { low[idx] = min(low[idx], ord[t]); }        }        is_articulation |= par == -1 && cnt > 1;        if (is_articulation) articulation.push_back(idx);        return k;    }    virtual void build() {        used.assign(g.n, 0);        ord.assign(g.n, 0);        low.assign(g.n, 0);        int k = 0;        for (int i = 0; i < g.n; i++) { if (!used[i]) k = dfs(i, k, -1); }    }};
template<typename T = int> class scc_un : LowLink<T> { /****************************************************************************/using LL = LowLink<T>;using LL::g;void dfs(int idx, int par, int &k) {        if (~par && this->ord[par] >= this->low[idx]) bel[idx] = bel[par];        else bel[idx] = k++;        forg(gi, g[idx]){            if (bel[t] == -1) dfs(t, idx, k);        }    }
public :
    int operator[](const int &k) {return bel[k];}
    void build(undigraph<> &comp) {        LL::build();        bel.assign(this->g.size(), -1);        int k = 0;        for (int i = 0; i < bel.size(); i++) {            if (bel[i] == -1) dfs(i, -1, k);        }        comp.resize(k);        for (auto &e : this->bridge) {            int x = bel[e.first], y = bel[e.second];            comp.add(x, y);        }        list.resize(sz(bel));        rep(i, bel.size()) {            list[bel[i]].push_back(i);        }    }
    // scc_un(undigraph<> &g) : LL(g) {}
    scc_un(undigraph<> &g, undigraph<> &comp) : LL(g) { build(comp); }

    vi bel;          //[i]  := iが所属するグループid
    vector<vi> list; //[gi] := giに所属する頂点集合
};
undigraph<> g(k5);//nにresizeしないとバグる
undigraph<> comp(0);//縮約後のグラフ をもつ
struct hld {/*@formatter:off*/
    int n,pos;
    undigraph<> G;
    vector<int> vid, head, sub, hvy, par, dep, inv, type;
    hld(undigraph<> g):n(g.n),pos(0),vid(n,-1),head(n),sub(n,1),hvy(n,-1),par(n),dep(n),inv(n),type(n),G(g){build( );}
    void build(vector<int> rs=vector<int>(1,0)) {        int c=0;        for(int r:rs){            dfs(r);            bfs(r, c++);        }    }    void dfs(int rt) {        using T = pair<int,int>;        stack<T> st;        par[rt]=-1;        dep[rt]=0;        st.emplace(rt,0);        while(!st.empty()){            int v=st.top().first;            int &i=st.top().second;            if(i<(int)G[v].size()){                int u=G[v][i++].t;                if(u==par[v]) continue;                par[u]=v;                dep[u]=dep[v]+1;                st.emplace(u,0);            }else{                st.pop();                int res=0;                forg(gi, G[v]){                    int u=t;                    if(u==par[v]) continue;                    sub[v]+=sub[u];                    if(res<sub[u]) res=sub[u],hvy[v]=u;                }            }        }    }    void bfs(int r,int c) {        int &k=pos;        queue<int> q({r});        while(!q.empty()){            int h=q.front();q.pop();            for(int i=h;i!=-1;i=hvy[i]) {                type[i]=c;                vid[i]=k++;                inv[vid[i]]=i;                head[i]=h;                forg(gi, G[i])if(t!=par[i]&&t!=hvy[i]) q.push(t);            }        }    }
    //[l,r)
    void for_each_(int u, int v, const function<void(int, int)> &f) {        while (1) {            if (vid[u] > vid[v]) swap(u, v);            f(max(vid[head[v]], vid[u]), vid[v]+1);            if (head[u] != head[v]) v = par[head[v]]; else break;        }    }
    void for_each_edge(int u, int v, const function<void(int, int)> &f) {        while (1) {            if (vid[u] > vid[v]) swap(u, v);            if (head[u] != head[v]) {                f(vid[head[v]], vid[v]+1);                v = par[head[v]];            }            else {                if (u != v) f(vid[u] + 1, vid[v]+1);                break;            }        }    }
    int lca(int u,int v){while(1){            if(vid[u]>vid[v]) swap(u,v);            if(head[u]==head[v]) return u;            v=par[head[v]];        }}
    int dis(int u,int v){return dep[u]+dep[v]-2*dep[lca(u,v)];}/*@formatter:on*/
    //辺のクエリを扱うとき
    //どの頂点に持たせればいいか(vidを返すのでそのままupd出来る)
    template<class T> int epos(int f, int t) { return dep[f] > dep[t] ? vid[f] : vid[t]; }
    template<class T> int epos(edge<T> &e) { return dep[e.f] > dep[e.t] ? vid[e.f] : vid[e.t]; }
    int operator[](int i) { return vid[i]; }
};
//半開区間
//半開区間
//半開区間
//半開区間
//@formatter:off
template<class M> struct segmax {
    int n;
    vector<M> seg;
    M f(M a,M b){        return a > b ? a : b;    }
    const M e = MIN(M);
    segmax(vector<M> dat) {        n = 1;        int asz = dat.size();        while (n <= asz)n <<= 1;        seg.assign((n << 1) - 1, e);        rep(i, asz) seg[i + n - 1] = dat[i];        rer(i, n - 2)seg[i] = f(seg[(i << 1) | 1], seg[(i << 1) + 2]);    }
    void update(int k, M v) {        seg[k + n - 1] = v;        k += n - 1;        while (k) {            k = (k - 1) >> 1;            seg[k] = f(seg[(k << 1) | 1], seg[(k << 1) + 2]);        }    }
    void del(int k) { update(k, e); }
    void add(int k, int v) { update(k, v + seg[k + n - 1]); }
    //高速なquery 葉から辿る
    M query_bottomup(int l, int r) {        M retl = e;        M retr = e;        l += n - 1;        r += n - 1;        while (l < r) {            /*右なら、次に右上へ移動してしまうので*/            if (!(l & 1)) { retl = f(retl, seg[l]); }            /*右なら、左を取らないと機会を逃す*/            if (!(r & 1)) { retr = f(seg[r - 1], retr); }            l >>= 1;            r = (r - 1) >> 1;        }        return f(retl, retr);    }
    M query(int a, int b, int k, int l, int r) {        if (r <= a || b <= l)return e;        else if (a <= l && r <= b)return seg[k];        else {            M sl = query(a, b, (k << 1) | 1, l, (l + r) >> 1);            M sr = query(a, b, (k << 1) + 2, (l + r) >> 1, r);            return f(sl, sr);        }    }
    //***************************
    //入れ替えることでbottomupと入れ替えられる
//    M get(int a = 0, int b = -1) { return query(a, b == -1 ? n : b, 0, 0, n); }
        M get(int a , int b ) { return query_bottomup(a, min(b,n));}
        M get(int b=inf ) { return query_bottomup(0, min(b,n));}
    //***************************
    int operator()(int a = 0, int b = inf) { return get(a, b); }
    M operator[](int k) { return seg[k + n - 1]; }
#ifdef _DEBUG
    void debu() {        rep(i, min(n, 10ll)) {            int v = operator[](i);            if (v == MIN(ll) || v == MAX(ll)) {                cerr << "e ";            } else {                cerr << v << " ";            }        }        cerr << "" << endl;    }
#else
    inline void debu(){;}
#endif
};
//@formatter:on

void solve() {
    in(n, m, q);
    g.resize(n);
    rep(i, m) {
        int f, t;
        cin >> f >> t;
        --f, --t;
        g.add(f, t);
    }
    scc_un<int> sc(g, comp);
    segmax<int> seg(vi(k5, -1));
    hld hl(comp);
    mapi where;
    static priority_queue<int> qs[k5];//大きい順

    rep(i,q) {
        din(ty);
        if (ty == 1) {
            din(u, w);
            u--;
            u = sc.bel[u];
            u = hl.vid[u];
            if (qs[u].empty() || qs[u].top() < w) {
                seg.update(u, w);
            }
            where[w] = u;
            qs[u] .push( w);
        } else {
            dind(s, t);
            int ans = -1;
            auto f = [&](int l, int r) {
                ans = max(ans, seg.get(l, r ));
            };
            hl.for_each_(sc.bel[s], sc.bel[t], f);
            cout << ans << endl;
            if (~ans) {
                int p = where[ans];
                qs[p].pop();
                seg.update(p, qs[p].empty() ? -1 : qs[p].top());
            }
        }
    }
}


signed main() {
    solve();


    return 0;
}