/**
 * author:  tsuyu93
 * started: 2021-05-25  19:54:49
 * 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; }
#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);}
#ifdef __HOGE__
#pragma endregion
#endif

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

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]); }
};

//auto ans = g.query(u, v, identity, [&](int a, int b) { return seg.query(a, b); }, f(query of seg), Edge? );

//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）)
};
*/

//type 1
struct Rmatrixmultiple_SUQ{
    static constexpr int segtree_type = 1;
    using typeT = vector<vector<long long>>;
    using typeE = vector<vector<long long>>;
    static typeT e_t;
    static typeT e_e;
    static typeT func_tt(typeT a, typeT b){
      vector<vector<long long>> res(a.size(),vector<long long>(b.size(),0));
      for(int i = 0;i < a.size();i++){
        for(int j = 0;j < a.size();j++){
          for(int k = 0;k < b.size();k++){
            res[i][j] += (a[i][k] * b[k][j])%MOD;
            res[i][j] %= MOD;
          }
        }
      }
    return res;}
    static typeT func_te(typeT a, typeE b, int w){return b;}
    static typeE func_ee(typeE a, typeE b){return a;}
};
vector<vector<long long>> Rmatrixmultiple_SUQ::e_t;
vector<vector<long long>> Rmatrixmultiple_SUQ::e_e;

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

    ll N;
    cin >> N;

    vvll G(N);
    vll X(N-1),Y(N-1);
    rep(i,N-1){
      ll a,b;
      cin >> a >> b;
      G[a].emplace_back(b);
      G[b].emplace_back(a);
      X[i] = a,Y[i] = b;
    }

    HLDecomposition hld(G);
    hld.build();

    vvll identity(2,vll(2,0));
    identity[0][0] = 1;
    identity[1][1] = 1;

    Rmatrixmultiple_SUQ::e_t = identity;
    Rmatrixmultiple_SUQ::e_e = identity;

    segment_tree<Rmatrixmultiple_SUQ> seg(N,identity);

    ll Q;
    cin >> Q;
    while(Q--){
      char q;
      cin >> q;
      if(q=='x'){
        ll v;
        cin >> v;
        vvll m(2,vll(2,0));
        cin >> m[0][0] >> m[0][1] >> m[1][0] >> m[1][1];
        seg.apply(max(hld.in[X[v]],hld.in[Y[v]]),m);
      }else{
        ll u,v;
        cin >> u >> v;
        vector<vector<long long>> vec = hld.query(u,v,identity,[&](int a,int b){return seg.find(a,b);},
          [&](vector<vector<long long>> a,vector<vector<long long>> b){
            vector<vector<long long>> res(a.size(),vector<long long>(b.size()));
            for(int i = 0;i < a.size();i++){
              for(int j = 0;j < a[i].size();j++){
                for(int k = 0;k < b[j].size();k++){
                  res[i][j] += (a[i][k] * b[k][j])%MOD;
                  res[i][j] %= MOD;
                }
              }
            }
          return res;},true);

        cout << vec[0][0] << " " << vec[0][1] << " " << vec[1][0] << " " << vec[1][1] << endl;
      }
    }

    //cout << ans << endl;

  return 0;
}