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

#ifndef LOCAL_TEST
#pragma GCC target ("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#endif // LOCAL_TEST

using ll = long long;
using pii = pair<int, int>; using pll = pair<ll, ll>;
using vi = vector<int>;  using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>;  using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
using vs = vector<string>; using vvs = vector<vector<string>>; using vvvs = vector<vector<vector<string>>>;

template<typename T> vector<vector<T>> vv(int h, int w, T val = T()) { return vector(h, vector<T>(w, val)); }
template<typename T> vector<vector<vector<T>>> vvv(int h1, int h2, int h3, T val = T()) { return vector(h1, vector(h2, vector<T>(h3, val))); }
template<typename T> vector<vector<vector<vector<T>>>> vvvv(int h1, int h2, int h3, int h4, T val = T()) { return vector(h1, vector(h2, vector(h3, vector<T>(h4, val)))); }

template <class T> using priority_queue_min = priority_queue<T, vector<T>, greater<T>>;

constexpr double PI = 3.14159265358979323;
constexpr int INF = 100100111; constexpr ll INFL = 3300300300300300491LL;
float EPS = 1e-8; double EPSL = 1e-10;


struct Nyan { Nyan() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } nyan;

#define all(a) (a).begin(), (a).end()
#define len(x) ((ll)(x).size())
#define sz(x) ((ll)(x).size())
#define rep1(n) for(ll dummy_iter = 0LL; dummy_iter < n; ++dummy_iter) // 0,1,...,n-1
#define rep2(i, n) for(ll i = 0LL, i##_counter = 0LL; i##_counter < ll(n); ++(i##_counter), (i) = i##_counter) // i=0,1,...,n-1
#define rep3(i, s, t) for(ll i = ll(s), i##_counter = ll(s); i##_counter < ll(t); ++(i##_counter), (i) = (i##_counter)) // i=s,s+1,...,t-1
#define rep4(i, s, t, step) for(ll i##_counter = step > 0 ? ll(s) : -ll(s), i##_end = step > 0 ? ll(t) : -ll(t), i##_step = abs(step), i = ll(s); i##_counter < i##_end; i##_counter += i##_step, i = step > 0 ? i##_counter : -i##_counter) // i=s,s+step,...,<t
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define repe(a, v) for(auto& a : (v)) // iterate over all elements in v
#define smod(n, m) ((((n) % (m)) + (m)) % (m))
#define sdiv(n, m) (((n) - smod(n, m)) / (m))
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());}

int Yes(bool b=true) { cout << (b ? "Yes\n" : "No\n"); return 0; };
int YES(bool b=true) { cout << (b ? "YES\n" : "NO\n"); return 0; };
int No(bool b=true) {return Yes(!b);};
int NO(bool b=true) {return YES(!b);};

template<typename T, size_t N> T max(array<T, N>& a) { return *max_element(all(a)); };
template<typename T, size_t N> T min(array<T, N>& a) { return *min_element(all(a)); };
template<typename T> T max(vector<T>& a) { return *max_element(all(a)); };
template<typename T> T min(vector<T>& a) { return *min_element(all(a)); };
template<typename T> vector<T> vec_slice(const vector<T>& a, int l, int r) { vector<T> rev; rep(i, l, r) rev.push_back(a[i]); return rev; };
template<typename T> T sum(vector<T>& a, T zero = T(0)) { T rev = zero; rep(i, sz(a)) rev += a[i]; return rev; };

template <class T> inline vector<T>& operator--(vector<T>& v) { repe(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repe(x, v) ++x; return v; }

ll powm(ll a, ll n, ll mod=INFL) {
    ll res = 1;
    while (n > 0) {
        if (n & 1) res = (res * a) % mod;
        if (n > 1) a = (a * a) % mod;
        n >>= 1;
    }
    return res;
}
ll sqrtll(ll x) {
    assert(x >= 0);
    ll rev = sqrt(x);
    while(rev * rev > x) --rev;
    while((rev+1) * (rev+1)<=x) ++rev;
    return rev;
}

template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; }
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; }

template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p);
template <class T> inline istream& operator>>(istream& is, vector<T>& v);
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p);
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v);
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp);
template <typename T> ostream &operator<<(ostream &os, const set<T> &st);
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st);
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st);
template <typename T> ostream &operator<<(ostream &os, deque<T> q);
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq);

template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repe(x, v) is >> x; return is; }
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p) { os << p.first << " " << p.second; return os; }
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v) { rep(i, sz(v)) { os << v.at(i); if (i != sz(v) - 1) os << " "; } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st) { ll cnt = 0; for (auto &e : st) { os << e << (++cnt != (int)st.size() ? " " : ""); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q) { while (q.size()) { os << q.front(); q.pop_front(); if (q.size()) os << " "; } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq) { while (pq.size()) { os << pq.top() << " "; pq.pop(); } return os; }
#define dout(x) cout << fixed << setprecision(10) << x << endl

#define read1(a) cin >> a;
#define read2(a, b) cin >> a >> b;
#define read3(a, b, c) cin >> a >> b >> c;
#define read4(a, b, c, d) cin >> a >> b >> c >> d;
#define read5(a, b, c, d, e) cin >> a >> b >> c >> d >> e;
#define read6(a, b, c, d, e, f) cin >> a >> b >> c >> d >> e >> f;
#define read7(a, b, c, d, e, f, g) cin >> a >> b >> c >> d >> e >> f >> g;
#define read8(a, b, c, d, e, f, g, h) cin >> a >> b >> c >> d >> e >> f >> g >> h;

#define overload_read(a, b, c, d, e, f, g, h, i, ...) i
#define read(...) overload_read(__VA_ARGS__,read8,read7,read6,read5,read4,read3,read2,read1)(__VA_ARGS__)

#define inner_output1(a) cout << a << endl;
#define inner_output2(a, b) cout << a << " " << b << endl;
#define inner_output3(a, b, c) cout << a << " " << b << " " << c << endl;
#define inner_output4(a, b, c, d) cout << a << " " << b << " " << c << " " << d << endl;
#define inner_output5(a, b, c, d, e) cout << a << " " << b << " " << c << " " << d << " " << e << endl;
#define inner_output6(a, b, c, d, e, f) cout << a << " " << b << " " << c << " " << d << " " << e << " " << f << endl;
#define inner_output7(a, b, c, d, e, f, g) cout << a << " " << b << " " << c << " " << d << " " << e << " " << f << " " << g << endl;
#define inner_output8(a, b, c, d, e, f, g, h) cout << a << " " << b << " " << c << " " << d << " " << e << " " << f << " " << g << " " << h << endl;

#define overload_inner_output(a, b, c, d, e, f, g, h, i, ...) i
#define out(...) overload_inner_output(__VA_ARGS__,inner_output8,inner_output7,inner_output6,inner_output5,inner_output4,inner_output3,inner_output2,inner_output1)(__VA_ARGS__)

#define ii(...) ll __VA_ARGS__; read(__VA_ARGS__)
#define si(...) string __VA_ARGS__; read(__VA_ARGS__)
#define ci(...) char __VA_ARGS__; read(__VA_ARGS__)
#define di(...) double __VA_ARGS__; read(__VA_ARGS__)
#define li(name,size); vector<ll> name(size); read(name)
#define lli(name,H,W); vector name(H,vector<ll>(W));rep(i,H) cin >> name[i];


#ifdef LOCAL_TEST
#define inner_debug1(a) cerr << "[DEBUG#" << __LINE__ << "] " << #a << " = " << a << endl;
#define inner_debug2(a, b) cerr << "[DEBUG#" << __LINE__ << "] "<< #a << " = " << a << ", " << #b << " = " << b << endl;
#define inner_debug3(a, b, c) cerr << "[DEBUG#" << __LINE__ << "] "<< #a << " = " << a << ", " << #b << " = " << b << ", " << #c << " = " << c << endl;
#define inner_debug4(a, b, c, d) cerr << "[DEBUG#" << __LINE__ << "] "<< #a << " = " << a << ", " << #b << " = " << b << ", " << #c << " = " << c << ", " << #d << " = " << d << endl;
#define inner_debug5(a, b, c, d, e) cerr << "[DEBUG#" << __LINE__ << "] "<< #a << " = " << a << ", " << #b << " = " << b << ", " << #c << " = " << c << ", " << #d << " = " << d << ", " << #e << " = " << e << endl;
#define inner_debug6(a, b, c, d, e, f) cerr << "[DEBUG#" << __LINE__ << "] "<< #a << " = " << a << ", " << #b << " = " << b << ", " << #c << " = " << c << ", " << #d << " = " << d << ", " << #e << " = " << e << ", " << #f << " = " << f << endl;
#define inner_debug7(a, b, c, d, e, f, g) cerr << "[DEBUG#" << __LINE__ << "] "<< #a << " = " << a << ", " << #b << " = " << b << ", " << #c << " = " << c << ", " << #d << " = " << d << ", " << #e << " = " << e << ", " << #f << " = " << f << ", " << #g << " = " << g << endl;
#define inner_debug8(a, b, c, d, e, f, g, h) cerr << "[DEBUG#" << __LINE__ << "] "<< #a << " = " << a << ", " << #b << " = " << b << ", " << #c << " = " << c << ", " << #d << " = " << d << ", " << #e << " = " << e << ", " << #f << " = " << f << ", " << #g << " = " << g << ", " << #h << " = " << h << endl;

#define overload_inner_debug(a, b, c, d, e, f, g, h, i, ...) i
#define debug(...) overload_inner_debug(__VA_ARGS__,inner_debug8,inner_debug7,inner_debug6,inner_debug5,inner_debug4,inner_debug3,inner_debug2,inner_debug1)(__VA_ARGS__)

#else
#define debug(...);
#endif // LOCAL_TEST


inline ll ctz(ll x) { return __builtin_ctzll(x);}
inline ll clz(ll x) { return __builtin_clzll(x);}
inline ll popcount(ll x) { return __builtin_popcountll(x);}
inline bool inrange(ll x, ll a, ll b) { return a <= x && x < b; }
template <typename T> inline ll findll(vector<T>& v, T x) { auto tmp = find(all(v), x);if(tmp == v.end()){return -1;}else{return distance(v.begin(),tmp); }}
inline ll findll(string& s, char x) { auto tmp = find(all(s), x);if(tmp == s.end()){return -1;}else{return distance(s.begin(),tmp); }}
#include <vector>
#include <utility>
#include <cassert>
#include <utility>
#include <vector>
#include <algorithm>

namespace nachia{

template<class Elem>
class CsrArray{
public:
    struct ListRange{
        using iterator = typename std::vector<Elem>::iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        Elem& operator[](int i) const { return begi[i]; }
    };
    struct ConstListRange{
        using iterator = typename std::vector<Elem>::const_iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        const Elem& operator[](int i) const { return begi[i]; }
    };
private:
    int m_n;
    std::vector<Elem> m_list;
    std::vector<int> m_pos;
public:
    CsrArray() : m_n(0), m_list(), m_pos() {}
    static CsrArray Construct(int n, std::vector<std::pair<int, Elem>> items){
        CsrArray res;
        res.m_n = n;
        std::vector<int> buf(n+1, 0);
        for(auto& [u,v] : items){ ++buf[u]; }
        for(int i=1; i<=n; i++) buf[i] += buf[i-1];
        res.m_list.resize(buf[n]);
        for(int i=(int)items.size()-1; i>=0; i--){
            res.m_list[--buf[items[i].first]] = std::move(items[i].second);
        }
        res.m_pos = std::move(buf);
        return res;
    }
    static CsrArray FromRaw(std::vector<Elem> list, std::vector<int> pos){
        CsrArray res;
        res.m_n = pos.size() - 1;
        res.m_list = std::move(list);
        res.m_pos = std::move(pos);
        return res;
    }
    ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    int size() const { return m_n; }
    int fullSize() const { return (int)m_list.size(); }
};

} // namespace nachia

namespace nachia{


struct Graph {
public:
    struct Edge{
        int from, to;
        void reverse(){ std::swap(from, to); }
        int xorval() const { return from ^ to; }
    };
    Graph(int n = 0, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {}
    Graph(int n, const std::vector<std::pair<int, int>>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){
        m_e.resize(edges.size());
        for(std::size_t i=0; i<edges.size(); i++) m_e[i] = { edges[i].first, edges[i].second };
    }
    template<class Cin>
    static Graph Input(Cin& cin, int n, bool undirected, int m, int offset = 0){
        Graph res(n, undirected, m);
        for(int i=0; i<m; i++){
            int u, v; cin >> u >> v;
            res[i].from = u - offset;
            res[i].to = v - offset;
        }
        return res;
    }
    int numVertices() const noexcept { return m_n; }
    int numEdges() const noexcept { return int(m_e.size()); }
    int addNode() noexcept { return m_n++; }
    int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; }
    Edge& operator[](int ei) noexcept { return m_e[ei]; }
    const Edge& operator[](int ei) const noexcept { return m_e[ei]; }
    Edge& at(int ei) { return m_e.at(ei); }
    const Edge& at(int ei) const { return m_e.at(ei); }
    auto begin(){ return m_e.begin(); }
    auto end(){ return m_e.end(); }
    auto begin() const { return m_e.begin(); }
    auto end() const { return m_e.end(); }
    bool isUndirected() const noexcept { return m_isUndir; }
    void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); }
    void contract(int newV, const std::vector<int>& mapping){
        assert(numVertices() == int(mapping.size()));
        for(int i=0; i<numVertices(); i++) assert(0 <= mapping[i] && mapping[i] < newV);
        for(auto& e : m_e){ e.from = mapping[e.from]; e.to = mapping[e.to]; }
        m_n = newV;
    }
    std::vector<Graph> induce(int num, const std::vector<int>& mapping) const {
        int n = numVertices();
        assert(n == int(mapping.size()));
        for(int i=0; i<n; i++) assert(-1 <= mapping[i] && mapping[i] < num);
        std::vector<int> indexV(n), newV(num);
        for(int i=0; i<n; i++) if(mapping[i] >= 0) indexV[i] = newV[mapping[i]]++;
        std::vector<Graph> res; res.reserve(num);
        for(int i=0; i<num; i++) res.emplace_back(newV[i], isUndirected());
        for(auto e : m_e) if(mapping[e.from] == mapping[e.to] && mapping[e.to] >= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]);
        return res;
    }
    CsrArray<int> getEdgeIndexArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(int i=0; i<numEdges(); i++){
            auto e = operator[](i);
            src.emplace_back(e.from, i);
            if(undirected) src.emplace_back(e.to, i);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); }
    CsrArray<int> getAdjacencyArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(auto e : m_e){
            src.emplace_back(e.from, e.to);
            if(undirected) src.emplace_back(e.to, e.from);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); }
private:
    int m_n;
    std::vector<Edge> m_e;
    bool m_isUndir;
};

} // namespace nachia
#include <vector>
#include <algorithm>

namespace nachia{

struct HeavyLightDecomposition{
private:

    int N;
    std::vector<int> P;
    std::vector<int> PP;
    std::vector<int> PD;
    std::vector<int> D;
    std::vector<int> I;

    std::vector<int> rangeL;
    std::vector<int> rangeR;

public:

    HeavyLightDecomposition(const CsrArray<int>& E = CsrArray<int>::Construct(1, {}), int root = 0){
        N = E.size();
        P.assign(N, -1);
        I = {root};
        I.reserve(N);
        for(int i=0; i<(int)I.size(); i++){
            int p = I[i];
            for(int e : E[p]) if(P[p] != e){
                I.push_back(e);
                P[e] = p;
            }
        }
        std::vector<int> Z(N, 1);
        std::vector<int> nx(N, -1);
        PP.resize(N);
        for(int i=0; i<N; i++) PP[i] = i;
        for(int i=N-1; i>=1; i--){
            int p = I[i];
            Z[P[p]] += Z[p];
            if(nx[P[p]] == -1) nx[P[p]] = p;
            if(Z[nx[P[p]]] < Z[p]) nx[P[p]] = p;
        }

        for(int p : I) if(nx[p] != -1) PP[nx[p]] = p;

        PD.assign(N,N);
        PD[root] = 0;
        D.assign(N,0);
        for(int p : I) if(p != root){
            PP[p] = PP[PP[p]];
            PD[p] = std::min(PD[PP[p]], PD[P[p]]+1);
            D[p] = D[P[p]]+1;
        }
        
        rangeL.assign(N,0);
        rangeR.assign(N,0);
        
        for(int p : I){
            rangeR[p] = rangeL[p] + Z[p];
            int ir = rangeR[p];
            for(int e : E[p]) if(P[p] != e) if(e != nx[p]){
                rangeL[e] = (ir -= Z[e]);
            }
            if(nx[p] != -1){
                rangeL[nx[p]] = rangeL[p] + 1;
            }
        }

        I.resize(N);
        for(int i=0; i<N; i++) I[rangeL[i]] = i;
    }
    
    HeavyLightDecomposition(const Graph& tree, int root = 0)
        : HeavyLightDecomposition(tree.getAdjacencyArray(true), root) {}

    int numVertices() const { return N; }
    int depth(int p) const { return D[p]; }
    int toSeq(int vtx) const { return rangeL[vtx]; }
    int toVtx(int seqidx) const { return I[seqidx]; }
    int toSeq2In(int vtx) const { return rangeL[vtx] * 2 - D[vtx]; }
    int toSeq2Out(int vtx) const { return rangeR[vtx] * 2 - D[vtx] - 1; }
    int parentOf(int v) const { return P[v]; }
    int heavyRootOf(int v) const { return PP[v]; }
    int heavyChildOf(int v) const {
        if(toSeq(v) == N-1) return -1;
        int cand = toVtx(toSeq(v) + 1);
        if(PP[v] == PP[cand]) return cand;
        return -1;
    }

    int lca(int u, int v) const {
        if(PD[u] < PD[v]) std::swap(u, v);
        while(PD[u] > PD[v]) u = P[PP[u]];
        while(PP[u] != PP[v]){ u = P[PP[u]]; v = P[PP[v]]; }
        return (D[u] > D[v]) ? v : u;
    }

    int dist(int u, int v) const {
        return depth(u) + depth(v) - depth(lca(u,v)) * 2;
    }

    struct Range{
        int l; int r;
        int size() const { return r-l; }
        bool includes(int x) const { return l <= x && x < r; }
    };

    std::vector<Range> path(int r, int c, bool include_root = true, bool reverse_path = false) const {
        if(PD[c] < PD[r]) return {};
        std::vector<Range> res(PD[c]-PD[r]+1);
        for(int i=0; i<(int)res.size()-1; i++){
            res[i] = { rangeL[PP[c]], rangeL[c]+1 };
            c = P[PP[c]];
        }
        if(PP[r] != PP[c] || D[r] > D[c]) return {};
        res.back() = { rangeL[r]+(include_root?0:1), rangeL[c]+1 };
        if(res.back().l == res.back().r) res.pop_back();
        if(!reverse_path) std::reverse(res.begin(),res.end());
        else for(auto& a : res) a = { N - a.r, N - a.l };
        return res;
    }

    Range subtree(int p) const { return { rangeL[p], rangeR[p] }; }

    int median(int x, int y, int z) const {
        return lca(x,y) ^ lca(y,z) ^ lca(x,z);
    }

    int la(int from, int to, int d) const {
        if(d < 0) return -1;
        int g = lca(from,to);
        int dist0 = D[from] - D[g] * 2 + D[to];
        if(dist0 < d) return -1;
        int p = from;
        if(D[from] - D[g] < d){ p = to; d = dist0 - d; }
        while(D[p] - D[PP[p]] < d){
            d -= D[p] - D[PP[p]] + 1;
            p = P[PP[p]];
        }
        return I[rangeL[p] - d];
    }

    struct ChildrenIterRange {
    struct Iter {
        const HeavyLightDecomposition& hld; int s;
        int operator*() const { return hld.toVtx(s); }
        Iter& operator++(){
            s += hld.subtree(hld.I[s]).size();
            return *this;
        }
        Iter operator++(int) const { auto a = *this; return ++a; }
        bool operator==(Iter& r) const { return s == r.s; }
        bool operator!=(Iter& r) const { return s != r.s; }
    };
        const HeavyLightDecomposition& hld; int v;
        Iter begin() const { return { hld, hld.rangeL[v] + 1 }; }
        Iter end() const { return { hld, hld.rangeR[v] }; }
    };
    ChildrenIterRange children(int v) const {
        return ChildrenIterRange{ *this, v };
    }
};

} // namespace nachia

#include <algorithm>
#include <cassert>
#include <vector>

namespace atcoder {

struct dsu {
  public:
    dsu() : _n(0) {}
    explicit dsu(int n) : _n(n), parent_or_size(n, -1) {}

    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }

    bool same(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }

    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }

    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }

    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                           [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }

  private:
    int _n;
    std::vector<int> parent_or_size;
};

}  // namespace atcoder


#include <algorithm>
#include <cassert>
#include <functional>
#include <vector>


#ifdef _MSC_VER
#include <intrin.h>
#endif

#if __cplusplus >= 202002L
#include <bit>
#endif

namespace atcoder {

namespace internal {

#if __cplusplus >= 202002L

using std::bit_ceil;

#else

unsigned int bit_ceil(unsigned int n) {
    unsigned int x = 1;
    while (x < (unsigned int)(n)) x *= 2;
    return x;
}

#endif

int countr_zero(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

constexpr int countr_zero_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

}  // namespace internal

}  // namespace atcoder


namespace atcoder {

#if __cplusplus >= 201703L

template <class S,
          auto op,
          auto e,
          class F,
          auto mapping,
          auto composition,
          auto id>
struct lazy_segtree {
    static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
                  "op must work as S(S, S)");
    static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
                  "e must work as S()");
    static_assert(
        std::is_convertible_v<decltype(mapping), std::function<S(F, S)>>,
        "mapping must work as F(F, S)");
    static_assert(
        std::is_convertible_v<decltype(composition), std::function<F(F, F)>>,
        "compostiion must work as F(F, F)");
    static_assert(std::is_convertible_v<decltype(id), std::function<F()>>,
                  "id must work as F()");

#else

template <class S,
          S (*op)(S, S),
          S (*e)(),
          class F,
          S (*mapping)(F, S),
          F (*composition)(F, F),
          F (*id)()>
struct lazy_segtree {

#endif

  public:
    lazy_segtree() : lazy_segtree(0) {}
    explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
    explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
        size = (int)internal::bit_ceil((unsigned int)(_n));
        log = internal::countr_zero((unsigned int)size);
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return e();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    void apply(int p, F f) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++) update(p >> i);
    }
    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    template <bool (*g)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G> int max_right(int l, G g) {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n) return _n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*g)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G> int min_left(int r, G g) {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;
    std::vector<F> lz;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
    void all_apply(int k, F f) {
        d[k] = mapping(f, d[k]);
        if (k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k) {
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }
};

}  // namespace atcoder

using namespace atcoder;
using namespace nachia;

ll op(ll a,ll b){
    return a+b;
}

ll e(){
    return 0;
}

ll mapping(ll f,ll x){
    if(f !=INFL ) return f;
    return x;
}

ll composition(ll f,ll g){
    if(f != INFL) return f;
    return g;
}

ll id(){
    return INFL;
}



int main(){
    ii(Q);
    dsu uf(200000);
    vector<pll> edges;
    vector<ll> first(200000,-1);
    vector<ll> time(200000,INFL);
    vector<pll> querys;
    ll cnt = 200000;
    rep(i,Q){
        ii(a,b);
        a--;b--;
        b+=100000;
        querys.emplace_back(a,b);
        if(uf.same(a,b)){
            if(first[uf.leader(a)] == -1){
                first[uf.leader(a)] = a;
                time[uf.leader(a)] = i;
            }
        }else{
            ll t;
            ll f;
            if((first[uf.leader(a)] != -1)&&(first[uf.leader(b)] != -1)){
                a = first[uf.leader(a)];
                b = first[uf.leader(b)];
            }
            if(time[uf.leader(a)] < time[uf.leader(b)]){
                t = time[uf.leader(a)];
                f = first[uf.leader(a)];
            }else{
                t = time[uf.leader(b)];
                f = first[uf.leader(b)];
            }
            uf.merge(a,b);
            cnt--;
            edges.emplace_back(a,b);
            first[uf.leader(a)] = f;
            time[uf.leader(a)] = t; 
        }
    }
    Graph g(200001,true,0);
    vector<bool> alr(200000,false);
    ll debug_cnt = 0;
    rep(i,len(edges)){
        g.addEdge(edges[i].first,edges[i].second);
        debug_cnt++;
    }
    rep(i,200000){
        if(alr[uf.leader(i)]) continue;
        alr[uf.leader(i)] = true;
        if (first[uf.leader(i)] != -1){
            g.addEdge(first[uf.leader(i)],200000);
            debug_cnt++;
        }else{
            g.addEdge(i,200000);
            debug_cnt++;
        }
    }
    debug(edges.size()+cnt);
    debug(debug_cnt);
    HeavyLightDecomposition hld(g,200000);
    dsu uf2(200000);
    ll A = 0;
    ll B = 0;

    vl akiyo(200000,0);
    vl bkiyo(200000,0);
    vl acnt(200000,0);
    vl bcnt(200000,0);
    vb iscycle(200000,false);
    vl X(200000,-1);
    vl Y(200000,-1);
    vector<ll> first2(200000,-1);
    vector<ll> time2(200000,INFL);
    lazy_segtree<ll,op,e,ll,mapping,composition,id> sega(200001);
    lazy_segtree<ll,op,e,ll,mapping,composition,id> segb(200001);
    rep(i,100000){
        acnt[i] = 1;
        sega.set(hld.toSeq(i),1);
        X[i] = i;
        Y[i] = i;
        bcnt[i+100000] = 1;
        segb.set(hld.toSeq(i+100000),1);
        X[i+100000] = i+100000;
        Y[i+100000] = i+100000;
    }

    debug("end_init");
    


    rep(i,Q){
        auto [a,b] = querys[i];
        if(uf2.same(a,b)){
            ll l = uf2.leader(a);
            if(first2[uf2.leader(a)] == -1){
                first2[uf2.leader(a)] = a;
                time2[uf2.leader(a)] = i;
            }
            if(!iscycle[uf2.leader(a)]){
                iscycle[l] = true;
                A -= akiyo[l];
                B -= bkiyo[l];
                akiyo[l] = acnt[l];
                bkiyo[l] = bcnt[l];
                A += akiyo[l];
                B += bkiyo[l];
            }
            ll lca = hld.lca(a,b);
            repe(R,hld.path(lca,first2[l],true,false)){
                ll tmp = sega.prod(R.l,R.r);
                akiyo[l] -= tmp;
                A -= tmp;
                sega.apply(R.l,R.r,0);

                tmp = segb.prod(R.l,R.r);
                bkiyo[l] -= tmp;
                B -= tmp;
                segb.apply(R.l,R.r,0);
            }
            repe(R,hld.path(lca,b,false,false)){
                ll tmp = sega.prod(R.l,R.r);
                akiyo[l] -= tmp;
                A -= tmp;
                sega.apply(R.l,R.r,0);

                tmp = segb.prod(R.l,R.r);
                bkiyo[l] -= tmp;
                B -= tmp;
                segb.apply(R.l,R.r,0);
            }
            
        }else{
            
            ll la = uf2.leader(a);
            ll lb = uf2.leader(b);
            debug(i,la,lb);
            ll fa = first2[uf2.leader(a)];
            ll fb = first2[uf2.leader(b)];
            ll ta = time2[uf2.leader(a)];
            ll tb = time2[uf2.leader(b)];

            ll t;
            ll f;
            if(time2[uf2.leader(a)] < time2[uf2.leader(b)]){
                t = time2[uf2.leader(a)];
                f = first2[uf2.leader(a)];
            }else{
                t = time2[uf2.leader(b)];
                f = first2[uf2.leader(b)];
            }
            uf2.merge(a,b);
            first2[uf2.leader(a)] = f;
            time2[uf2.leader(a)] = t; 
            ll newl = uf2.leader(a);


            if((!iscycle[la]) && (!iscycle[lb])){
                debug(i,la,lb);
                A -= akiyo[la];
                B -= bkiyo[la];
                A -= akiyo[lb];
                B -= bkiyo[lb];
                acnt[newl] = acnt[la] + acnt[lb];
                bcnt[newl] = bcnt[la] + bcnt[lb];

                ll x = -1;
                ll y = -1;
                ll v = -1;
                vl tmp = {X[la],X[lb],Y[la],Y[lb]};
                repe(l,tmp){
                    repe(r,tmp){
                        if (chmax(v,(ll)hld.dist(l,r))){
                            x = l;
                            y = r;
                        }   
                    }
                }
                X[newl] = x;
                Y[newl] = y;
                
                if ((x < 100000) && (y < 100000)){
                    //同じ色の場合
                    //必ず長さが偶数のはず。
                    assert(v%2 == 0);
                    if((v/2)%2 == 0){
                        akiyo[newl] = acnt[newl] - 1;
                        bkiyo[newl] = bcnt[newl];
                    }else{
                        akiyo[newl] = acnt[newl];
                        bkiyo[newl] = bcnt[newl] - 1;
                    }
                }else{
                    if(!((x >= 100000) && (y >= 100000))){
                        v--;
                    }
                    assert(v%2 == 0);
                    if((v/2)%2 == 0){
                        akiyo[newl] = acnt[newl];
                        bkiyo[newl] = bcnt[newl] - 1;
                    }else{
                        akiyo[newl] = acnt[newl] - 1;
                        bkiyo[newl] = bcnt[newl];
                    }

                }
                A += akiyo[newl];
                B += bkiyo[newl];

            }else if(iscycle[la] && iscycle[lb]){
                // faとfbをつなげる
                // aと根、bと根をつなげる
                akiyo[newl] = akiyo[la] + akiyo[lb];
                bkiyo[newl] = bkiyo[la] + bkiyo[lb];
                acnt[newl] = acnt[la] + acnt[lb];
                bcnt[newl] = bcnt[la] + bcnt[lb];

                ll lca = hld.lca(a,b);
                repe(R,hld.path(lca,first2[newl],true,false)){
                    ll tmp = sega.prod(R.l,R.r);
                    akiyo[newl] -= tmp;
                    A -= tmp;
                    sega.apply(R.l,R.r,0);

                    tmp = segb.prod(R.l,R.r);
                    bkiyo[newl] -= tmp;
                    B -= tmp;
                    segb.apply(R.l,R.r,0);
                }
                repe(R,hld.path(lca,b,false,false)){
                    ll tmp = sega.prod(R.l,R.r);
                    akiyo[newl] -= tmp;
                    A -= tmp;
                    sega.apply(R.l,R.r,0);

                    tmp = segb.prod(R.l,R.r);
                    bkiyo[newl] -= tmp;
                    B -= tmp;
                    segb.apply(R.l,R.r,0);
                }

            }else{
                if(!iscycle[la]){
                    swap(la,lb);
                    swap(fa,fb);
                    swap(ta,tb);
                }

                // laがサイクル
                A -= akiyo[lb];
                B -= bkiyo[lb];
                akiyo[newl] = akiyo[la] + acnt[lb];
                bkiyo[newl] = bkiyo[la] + bcnt[lb];
                A += acnt[lb];
                B += bcnt[lb];
                acnt[newl] = acnt[la] + acnt[lb];
                bcnt[newl] = bcnt[la] + bcnt[lb];
            }   
            
        }
        out(A,B);
    }

}