import static java.lang.Math.*; import static java.util.Arrays.*; import java.io.*; import java.lang.reflect.*; import java.util.*; import java.util.concurrent.*; import java.util.function.*; public final class Main{ public static void main(String[] args) throws Exception{ MyReader in = new MyReader(System.in); MyWriter out = new MyWriter(System.out,false),log = new MyWriter(System.err,true); int T = Solver.multi ? in.it() : 1; while (T-- > 0) Optional.ofNullable(new Solver(in,out,log).solve()).ifPresent(out::println); out.flush(); } } class Solver extends BaseSolver{ public Solver(MyReader in,MyWriter out,MyWriter log){ super(in,out,log); } public static boolean multi = false; public Object solve(){ int N = in.it(); int M = in.it(); int K = in.it(); long[] A = new long[1 <>= 1)); return ret; } } class MyDequeInt{ int[] arr = new int[16]; int hd = 0; int tl = 0; public MyDequeInt(int n){ arr = new int[n]; } void addFirst(int e){ hd = mod(hd -1); arr[hd] = e; if (hd == tl) resize(); } void addLast(int e){ arr[tl] = e; tl = mod(tl +1); if (hd == tl) resize(); } int peek(){ return peekFirst(); } int peekFirst(){ return arr[hd]; } int peekLast(){ return arr[tl]; } int poll(){ return pollFirst(); } int pollFirst(){ int ret = arr[hd]; hd = mod(hd +1); return ret; } int pollLast(){ tl = mod(tl -1); return arr[tl]; } int get(int i){ return arr[mod(hd +i)]; } int size(){ return mod(tl -hd); } boolean isEmpty(){ return tl == hd; } private int mod(int i){ return (i +arr.length) %arr.length; } private void resize(){ int[] newarr = new int[arr.length <<1]; System.arraycopy(arr,hd,newarr,0,arr.length -hd); System.arraycopy(arr,0,newarr,arr.length -hd,tl); hd = 0; tl = arr.length; arr = newarr; } } class Prime{ private long[] spf, arrI = {2, 7, 61}, arrL = {2, 325, 9375, 28178, 450775, 9780504, 1795265022}; public Prime(){ this(1_000_000); } public Prime(int n){ spf = new long[n +1]; Arrays.setAll(spf,i -> i); for (int p = 2;p *p <= n;p++) if (spf[p] == p) for (int l = p *p;l <= n;l += p) spf[l] = p; } public long[] divisors(long n){ long[] fs = factorize(n); int l = fs.length > 0 ? 2 : 1,id = 0; for (int i = 1,sz = 1;i < fs.length;i++,l += sz) if (fs[i -1] < fs[i]) sz = l; long[] ret = new long[l]; ret[id++] = 1; for (int i = 0,s = 0,sz = 1;i < fs.length;i++,s += sz) { if (0 < i && fs[i -1] < fs[i]) { sz = id; s = 0; } for (int j = s;j < s +sz;j++) ret[id++] = ret[j] *fs[i]; } sort(ret); return ret; } public long[] factorize(long n){ if (n < 2) return new long[0]; long[] ret = new long[64]; int h = 0,t = 0; ret[t++] = n; while (h < t) { long cur = ret[h++]; if (!isPrime(cur)) { var p = rho(cur); ret[--h] = p; ret[t++] = cur /p; } } sort(ret,0,t); return copyOf(ret,t); } public boolean isPrime(long n){ if (n < spf.length) return 1 < n && spf[(int) n] == n; if ((n &1) == 0) return false; ModInt bm = new ModInt(n); long lsb = n -1 &-n +1; long m = (n -1) /lsb; a:for (var a:n < 1 <<30 ? arrI : arrL) { long z = bm.pow(a %n,m); if (z < 2) continue; for (long k = 1;k <= lsb;k <<= 1) if (z == n -1) continue a; else z = bm.mul(z,z); return false; } return true; } private long rho(long n){ if (n < spf.length) return spf[(int) n]; if ((n &1) == 0) return 2; ModInt bm = new ModInt(n); for (long t;;) { long x = 0,y = x,q = 1,c = Util.rd.nextLong(n -1) +1; a:for (int k = 1;;k <<= 1,y = x,q = 1) for (int i = k;i-- > 0;) { x = bm.mul(x,x) +c; if (n <= x) x -= n; q = bm.mul(q,abs(x -y)); if ((i &127) == 0 && (t = gcd(q,n)) > 1) break a; } if (t < n) return t; } } private long gcd(long a,long b){ while (0 < b) { long t = a; a = b; b = t %b; } return a; } class ModInt{ private long n,r2,ni; public ModInt(long n){ this.n = n; r2 = (1L <<62) %n; for (int i = 0;i < 66;i++) { r2 <<= 1; if (r2 >= n) r2 -= n; } ni = n; for (int i = 0;i < 5;++i) ni *= 2 -n *ni; } private static long high(long x,long y){ return multiplyHigh(x,y) +(x >>63 &y) +(y >>63 &x); } private long mr(long x,long y){ return high(x,y) +high(-ni *x *y,n) +(x *y == 0 ? 0 : 1); } public long mod(long x){ return x < n ? x : x -n; } public long mul(long x,long y){ return mod(mr(mr(x,r2),y)); } public long pow(long x,long y){ long z = mr(x,r2); long r = 1; while (y > 0) { if ((y &1) == 1) r = mr(r,z); z = mr(z,z); y >>= 1; } return mod(r); } } } class Combin{ int n = 2; long[] f,fi; long mod = Util.mod; public Combin(int n){ this(); grow(n); } public Combin(){ f = fi = new long[]{1, 1}; } public void grow(int n){ n = min((int) mod,n); f = copyOf(f,n); fi = copyOf(fi,n); for (int i = this.n;i < n;i++) f[i] = f[i -1] *i %mod; fi[n -1] = pow(f[n -1],mod -2); for (int i = n;--i > this.n;) fi[i -1] = fi[i] *i %mod; this.n = n; } private long pow(long x,long n){ long ret = 1; for (x %= mod;0 < n;x = x *x %mod,n >>= 1) if ((n &1) == 1) ret = ret *x %mod; return ret; } public long nHr(int n,int r){ return r < 0 ? 0 : nCr(n +r -1,r); } public long nCr(int n,int r){ if (r < 0 || n -r < 0) return 0; if (this.n <= n) grow(max(this.n <<1,n +1)); return f[n] *(fi[r] *fi[n -r] %mod) %mod; } } class Data extends BaseV{ int v; public Data(int v){ this.v = v; } @Override public String toString(){ return "" +v; } } abstract class RelationalUnionFind extends UnionFind{ private F[] dist; @SuppressWarnings("unchecked") public RelationalUnionFind(int n){ super(n); dist = (F[]) new Object[n]; setAll(dist,i -> id()); } protected abstract F id(); protected abstract F comp(F a,F b); protected abstract F inv(F v); protected abstract boolean eq(F a,F b); @Override public int root(int x){ if (dat[x] < 0) return x; int r = root(dat[x]); dist[x] = comp(dist[dat[x]],dist[x]); return dat[x] = r; } public boolean valid(int u,int v,F c){ return !same(u,v) || eq(dist(u,v),c); } @Deprecated @Override public boolean unite(int u,int v){ return unite(u,v,id()); } public boolean unite(int u,int v,F f){ if (!valid(u,v,f)) return false; if (same(u,v)) return true; f = comp(dist(u),f); f = comp(f,inv(dist(v))); super.unite(u = root(u),v = root(v)); if (dat[u] > dat[v]) dist[u] = inv(f); else dist[v] = f; return true; } public F dist(int x){ root(x); return dist[x]; } public F dist(int u,int v){ return !same(u,v) ? null : comp(inv(dist(u)),dist(v)); } } abstract class DigitDp { private int B; private int[] N; private T[] dp; public DigitDp(char[] N){ this(N,10); } public DigitDp(char[] N,int B){ this.N = new int[N.length]; for (int i = 0;i < N.length;i++) this.N[i] = N[i] -'0'; dp = Util.cast(Array.newInstance(init().getClass(),N.length +1 <<1)); this.B = B; setAll(dp,i -> init()); } protected abstract T init(); protected abstract void f(T pd,T dp,int n,int k); protected void mod(T dp){} public T get(int i,int same){ return dp[i *2 +same]; } public void calc(){ for (int i = 0;i < N.length;i++) { int t = N[i]; for (int n = 0;n < B;n++) { if (n == t) f(get(i +1,1),get(i,1),n,N.length -1 -i); if (n < t) f(get(i +1,0),get(i,1),n,N.length -1 -i); if (0 < i) f(get(i +1,0),get(i,0),n,N.length -1 -i); } mod(get(i +1,0)); mod(get(i +1,1)); } } } abstract class Dijkstra extends Graph{ private Comparator cmp; private L[] len; private int[] hep,idx; private Edge[] pre; private int sz; public Dijkstra(int n,boolean dir){ super(n,dir); hep = new int[n]; idx = new int[n]; cmp = cmp(); } protected abstract L zero(); protected abstract L inf(); protected abstract L f(L l,Edge e); protected Comparator cmp(){ return Util.cast(Comparator.naturalOrder()); } public L[] calc(int s){ return calc(s,-1); } public L[] calc(int s,int g){ len = Util.cast(Array.newInstance(zero().getClass(),sz = n)); pre = Util.cast(new Edge[n]); fill(len,inf()); setAll(hep,i -> i); setAll(idx,i -> i); set(s,zero()); for (int cur;0 < sz && (cur = poll()) != g;) for (var e:go(cur)) set((pre[e.v] = e).v,f(len[cur],e)); return len; } public L get(int t){ return len[t]; } public Deque> path(int t){ Deque> ret = new ArrayDeque<>(); while (pre[t] != null) { ret.addFirst(pre[t]); t = pre[t].u; } return ret; } private void set(int i,L l){ if (idx[i] < sz && cmp.compare(l,len[i]) < 0) { len[i] = l; heapfy(idx[i]); } } private int poll(){ int ret = hep[0]; heapfy(swap(0,--sz)); return ret; } private void heapfy(int k){ int p = k -1 >>1; if (0 <= p && cmp.compare(len[hep[p]],len[hep[k]]) > 0) { heapfy(swap(p,k)); return; } int c = k <<1 |1; if (sz <= c) return; if (c +1 < sz && cmp.compare(len[hep[c]],len[hep[c +1]]) > 0) c++; if (cmp.compare(len[hep[c]],len[hep[k]]) < 0) heapfy(swap(c,k)); } private int swap(int i,int j){ hep[i] ^= hep[j]; hep[j] ^= hep[i]; hep[i] ^= hep[j]; idx[hep[i]] = i; idx[hep[j]] = j; return i; } } abstract class DualSegmentTree extends Seg{ public DualSegmentTree(int n){ super(n); } @Override protected void agg(V v,V a,V b){} @Override public void upd(int i,F f){ upd(i,i +1,f); } @Override public void upd(int l,int r,F f){ down(l,r); super.upd(l,r,f); } @Override public V get(int i){ down(i,i +1); return super.get(i); } } abstract class LazySegmentTree extends Seg{ public LazySegmentTree(int n){ super(n); } @Override public void upd(int i,F f){ upd(i,i +1,f); } @Override public void upd(int l,int r,F f){ down(l,r); super.upd(l,r,f); up(l,r); } @Override public V get(int i){ down(i,i +1); return super.get(i); } @Override public V get(int l,int r){ down(l,r); return super.get(l,r); } } abstract class Seg { private int n,log; private V[] val; private F[] lazy; protected Seg(int n){ this.n = n; while (1 < 0;merge(i)) (val[i] = e()).sz = val[i <<1].sz +val[i <<1 |1].sz; } public void upd(int i,F f){ prop(i +n,f); } public void upd(int l,int r,F f){ for (l += n,r += n;l < r;l >>= 1,r >>= 1) { if ((l &1) == 1) prop(l++,f); if ((r &1) == 1) prop(--r,f); } } public V get(int i){ return val[i +n]; } public V get(int l,int r){ V[] ret = Util.cast(new BaseV[]{e(), e()}); int i = 0; for (var v:getList(l,r)) { agg(ret[i],ret[i ^1],v); ret[i].sz = ret[i ^= 1].sz +v.sz; } return ret[i ^1]; } public V[] getList(int l,int r){ int sz = 0; for (int li = l += n,ri = r += n;li < ri;li = li +1 >>1,ri >>= 1) sz += (li &1) +(ri &1); V[] arr = Util.cast(Array.newInstance(e().getClass(),sz)); for (int i = 0;l < r;l >>= 1,r >>= 1) { if ((l &1) > 0) arr[i++] = val[l++]; if ((r &1) > 0) arr[--sz] = val[--r]; } return arr; } public V[] getPath(int i){ int sz = 32 -Integer.numberOfLeadingZeros(i +n); V[] arr = Util.cast(Array.newInstance(e().getClass(),sz)); for (i += n;0 < i;i >>= 1) arr[--sz] = val[i]; return arr; } protected V init(int i){ return e(); } protected abstract V e(); protected abstract void agg(V v,V a,V b); protected abstract void map(V v,F f); protected abstract F comp(F f,F g); protected void up(int l,int r){ for (l = oddPart(l +n),r = oddPart(r +n);l != r;) merge(l > r ? (l >>= 1) : (r >>= 1)); while (1 < l) merge(l >>= 1); } protected void down(int l,int r){ int i = log; for (l = oddPart(l +n),r = oddPart(r +n);i > 0;i--) { push(l >>i); push(r >>i); } } private void merge(int i){ agg(val[i],val[i <<1],val[i <<1 |1]); } private void push(int i){ if (lazy[i] != null) { prop(i <<1,lazy[i]); prop(i <<1 |1,lazy[i]); lazy[i] = null; } } private void prop(int i,F f){ map(val[i],f); if (i < n) { lazy[i] = lazy[i] == null ? f : comp(lazy[i],f); if (val[i].fail) { push(i); merge(i); } } } private int oddPart(int i){ return i /(i &-i); } } abstract class SegmentTree extends Seg{ public SegmentTree(int n){ super(n); } @Override protected F comp(F f,F g){ return null; } @Override public void upd(int i,F f){ super.upd(i,f); up(i,i +1); } } class UnionFind{ int num; protected int[] dat; protected int[] nxt; public UnionFind(int n){ dat = new int[n]; nxt = new int[n]; setAll(nxt,i -> i); fill(dat,-1); num = n; } public int root(int x){ return dat[x] < 0 ? x : (dat[x] = root(dat[x])); } public boolean same(int u,int v){ return root(u) == root(v); } public boolean unite(int u,int v){ if ((u = root(u)) == (v = root(v))) return false; if (dat[u] > dat[v]) { u ^= v; v ^= u; u ^= v; } dat[u] += dat[v]; dat[v] = u; num--; nxt[u] ^= nxt[v]; nxt[v] ^= nxt[u]; nxt[u] ^= nxt[v]; return true; } public int size(int x){ return -dat[root(x)]; } public int[] getGroup(int x){ int[] ret = new int[size(x)]; for (int i = 0,c = root(x);i < ret.length;i++) ret[i] = c = nxt[c]; return ret; } } abstract class ReRootingDp extends Graph{ private D[] dp; private A[] ans; public ReRootingDp(int N){ super(N,false); dp = Util.cast(new Object[2 *N]); ans = Util.cast(Array.newInstance(ans(0,e()).getClass(),n)); } protected abstract D e(); protected abstract D agg(D a,D b); protected abstract D adj(D v,Edge e); protected abstract A ans(int u,D sum); protected MyList sur(int u){ return go(u).map(e -> dp[e.id]); } public A[] calc(){ for (var e:es) e.re.id = e.id +n; var stk = new MyStack>(); var se = new Edge(n -1,-1,0,null); stk.add(se); while (!stk.isEmpty()) { var e = stk.pop(); if (dp[e.id] == null) { dp[e.id] = e(); for (var ee:go(e.v)) if (ee != e.re) { stk.add(ee); stk.add(ee); } } else { for (var ee:go(e.v)) if (ee != e.re) dp[e.id] = agg(dp[e.id],dp[ee.id]); if (e.u > -1) dp[e.id] = adj(dp[e.id],e); } } stk.add(se); while (!stk.isEmpty()) { var e = stk.pop(); var es = go(e.v); int n = es.size(); D[] pre = Util.cast(new Object[n +1]),suf = Util.cast(new Object[n +1]); pre[0] = e(); suf[n] = e(); for (int i = 0;i < n;i++) { pre[i +1] = agg(pre[i],dp[es.get(i).id]); suf[n -1 -i] = agg(dp[es.get(n -1 -i).id],suf[n -i]); } ans[e.v] = ans(e.v,suf[0]); for (int i = 0;i < n;i++) { Edge ee = es.get(i); if (ee != e.re) { dp[ee.re.id] = adj(agg(pre[i],suf[i +1]),ee.re); stk.add(ee); } } } return ans; } } class Edge { public int id,u,v; public L val; public Edge re; public Edge(int id,int u,int v,L val){ this.id = id; this.u = u; this.v = v; this.val = val; } } class Graph { public int n; public MyList> es; private MyList>[] go,bk; public Graph(int n,boolean dir){ this.n = n; go = Util.cast(new MyList[n]); bk = dir ? Util.cast(new MyList[n]) : go; for (int i = 0;i < n;i++) { go[i] = new MyList<>(); bk[i] = new MyList<>(); } es = new MyList<>(); } protected L inv(L l){ return l; } public void addEdge(int u,int v){ addEdge(u,v,null); } public void addEdge(int u,int v,L l){ var e = new Edge<>(es.size(),u,v,l); var re = new Edge<>(e.id,e.v,e.u,inv(e.val)); es.add(e); go[u].add(re.re = e); bk[v].add(e.re = re); } public MyList> go(int u){ return go[u]; } public MyList> bk(int u){ return bk[u]; } } abstract class AVLSegmentTree { private V e = e(),t = e(); private Node root; public AVLSegmentTree(int n){ root = new Node(e(),n); } public AVLSegmentTree(){} public void build(int n,IntFunction init){ root = build(0,n,init); } private Node build(int i,int n,IntFunction init){ if (n < 2) return n < 1 ? null : new Node(init.apply(i),1); var ret = new Node(e(),n); ret.cld(-1,build(i,n /2,init)); ret.cld(1,build(i +n /2,n -n /2,init)); return ret.merge(); } public void add(V v){ add(v,1); } public void add(V v,int k){ ins(size(),v,k); } public void ins(int i,V v){ ins(i,v,1); } public void ins(int i,V v,int k){ root = root == null ? new Node(v,k) : ins(root,i,v,k); } private Node ins(Node nd,int i,V v,int k){ if (nd.lft == null && (i == 0 || i == nd.sz)) { split(nd,i == 0 ? 1 : -1,v,k,nd.sz +k); return nd.merge(); } if (nd.lft == null) split(nd,1,ag(e(),e,nd.val),i,nd.sz); else nd.push(); if (i < nd.lft.sz) nd.cld(-1,ins(nd.lft,i,v,k)); else nd.cld(1,ins(nd.rht,i -nd.lft.sz,v,k)); return balance(nd); } public V del(int i){ var ret = e(); root = del(ret,root,i); return ret; } private Node del(V ret,Node nd,int i){ if (nd.lft == null) { nd.sz--; ag(ret,e,nd.val); return 0 < nd.sz ? nd : null; } nd.push(); int c = i < nd.lft.sz ? -1 : 1; Node del = c < 0 ? del(ret,nd.lft,i) : del(ret,nd.rht,i -nd.lft.sz); if (del == null) return nd.cld(-c); nd.cld(c,del); return balance(nd); } public void upd(int i,F f){ upd(i,i +1,f); } public void upd(int l,int r,F f){ if (l == r) return; if (size() < r) add(e(),r -size()); root = upd(root,l,r,f); } private Node upd(Node nd,int l,int r,F f){ if (l == 0 && r == nd.sz) return nd.prop(f); if (nd.lft == null) split(nd,1,ag(e(),e,nd.val),0 < l ? l : r,nd.sz); else nd.push(); if (l < nd.lft.sz) nd.cld(-1,upd(nd.lft,l,min(nd.lft.sz,r),f)); if (nd.lft.sz < r) nd.cld(1,upd(nd.rht,max(0,l -nd.lft.sz),r -nd.lft.sz,f)); return balance(nd); } public void toggle(int l,int r){ root = l < r ? toggle(root,l,r) : root; } private Node toggle(Node nd,int l,int r){ nd.push(); if (0 < l) { split(nd,l); return merge(nd.lft,nd,toggle(nd.rht,0,r -l)); } if (r < nd.sz) { split(nd,r); return merge(toggle(nd.lft,l,r),nd,nd.rht); } return nd.toggle(); } private void split(Node nd,int i){ if (nd.lft == null) split(nd,1,ag(e(),e,nd.val),i,nd.sz); else { nd.push(); if (i < nd.lft.sz) { split(nd.lft,i); var lft = nd.lft; nd.cld(-1,lft.lft); nd.cld(1,merge(lft.rht,lft,nd.rht)); } else if (nd.lft.sz < i) { split(nd.rht,i -nd.lft.sz); var rht = nd.rht; nd.cld(1,rht.rht); nd.cld(-1,merge(nd.lft,rht,rht.lft)); } } } private Node merge(Node lft,Node nd,Node rht){ if (abs(lft.rnk -rht.rnk) < 2) { nd.cld(-1,lft); nd.cld(1,rht); } else if (lft.rnk > rht.rnk) { lft.push().cld(1,merge(lft.rht,nd,rht)); nd = lft; } else if (lft.rnk < rht.rnk) { rht.push().cld(-1,merge(lft,nd,rht.lft)); nd = rht; } return balance(nd); } public V get(int i){ return get(i,i +1); } public V get(int l,int r){ V ret = e(); if (root != null) get(ret,root,l,min(r,size())); return ret; } private void get(V ret,Node nd,int l,int r){ if (l == 0 && r == nd.sz) ag(ret,ret,nd.val()); else if (nd.lft == null) ag(ret,ret,pw(nd.val,r -l)); else { nd.push(); if (l < nd.lft.sz) get(ret,nd.lft,l,min(nd.lft.sz,r)); if (nd.lft.sz < r) get(ret,nd.rht,max(0,l -nd.lft.sz),r -nd.lft.sz); } } public V all(){ return root == null ? e : root.val(); } public int size(){ return root == null ? 0 : root.sz; } protected abstract V e(); protected abstract void agg(V v,V a,V b); protected abstract void map(V v,F f); protected abstract F comp(F f,F g); protected abstract void tog(V v); private V ag(V v,V a,V b){ agg(v,a,b); v.sz = a.sz +b.sz; return v; } protected void pow(V v,V a,int n){ for (ag(t,e,a);0 < n;n >>= 1,ag(t,t,t)) if (0 < (n &1)) ag(v,v,t); } private V pw(V a,int n){ V ret = e(); pow(ret,a,n); ret.sz = n; return ret; } private void split(Node nd,int c,V vl,int i,int sz){ nd.cld(-c,new Node(vl,i)); nd.cld(c,new Node(nd.val,sz -i)); nd.val = e(); } private Node balance(Node nd){ return (1 < abs(nd.bis = nd.rht.rnk -nd.lft.rnk) ? (nd = rotate(nd)) : nd).merge(); } private Node rotate(Node u){ var v = u.cld(u.bis).push(); if (u.bis *v.bis < -1) v = rotate(v); u.cld(u.bis,v.cld(-u.bis)); v.cld(-u.bis,u); u.merge(); return v; } private class Node{ private int sz,bis,rnk,tog; private V val; private F laz; private Node lft,rht; private Node(V val,int sz){ this.sz = sz; this.val = val; val.sz = 1; } private Node merge(){ bis = rht.rnk -lft.rnk; rnk = max(lft.rnk,rht.rnk) +1; ag(val,lft.val(),rht.val()); sz = val.sz; return this; } private Node push(){ if (laz != null) { lft.prop(laz); rht.prop(laz); laz = null; } if (0 < tog) { lft.toggle(); rht.toggle(); tog = 0; } return this; } private Node prop(F f){ map(val,f); if (lft != null) laz = laz == null ? f : comp(laz,f); return this; } private Node toggle(){ bis *= -1; var tn = lft; lft = rht; rht = tn; tog(val); if (lft != null) tog ^= 1; return this; } private Node cld(int c){ return c < 0 ? lft : rht; } private void cld(int c,Node nd){ nd = c < 0 ? (lft = nd) : (rht = nd); } private V val(){ return lft == null && 1 < sz ? pw(val,sz) : val; } } } abstract class SparseTable2D{ int h,w,hl,wl; long[][][][] tbl; SparseTable2D(int h,int w){ hl = max(1,32 -Integer.numberOfLeadingZeros((this.h = h) -1)); wl = max(1,32 -Integer.numberOfLeadingZeros((this.w = w) -1)); tbl = new long[hl][wl][][]; for (int hi = 0;hi < hl;hi++) for (int wi = 0;wi < wl;wi++) { int hhl = h -(1 < extends MyList{ public T pop(){ return remove(size() -1); } public T peek(){ return get(size() -1); } } class MyList implements Iterable{ private T[] arr; private int sz; public MyList(){ this(16); } public MyList(int n){ arr = Util.cast(new Object[n]); } public boolean isEmpty(){ return sz == 0; } public int size(){ return sz; } public T get(int i){ return arr[i]; } public void add(T t){ (arr = sz < arr.length ? arr : copyOf(arr,sz *5 >>2))[sz++] = t; } public T remove(int i){ var ret = arr[i]; sz--; for (int j = i;j < sz;j++) arr[j] = arr[j +1]; return ret; } public T removeFast(int i){ var ret = arr[i]; arr[i] = arr[--sz]; return ret; } public void sort(){ sort(Util.cast(Comparator.naturalOrder())); } public void sort(Comparator cmp){ Arrays.sort(arr,0,sz,cmp); } @Override public Iterator iterator(){ return new Iterator<>(){ int i = 0; @Override public boolean hasNext(){ return i < sz; } @Override public T next(){ return arr[i++]; } }; } public MyList map(Function func){ MyList ret = new MyList<>(sz); forEach(t -> ret.add(func.apply(t))); return ret; } public T[] toArray(){ return copyOf(arr,sz); } public void swap(int i,int j){ var t = arr[i]; arr[i] = arr[j]; arr[j] = t; } public void set(int i,T t){ arr[i] = t; } } class BaseSolver extends Util{ public MyReader in; public MyWriter out,log; public BaseSolver(MyReader in,MyWriter out,MyWriter log){ this.in = in; this.out = out; this.log = log; } protected long inv(long x){ return pow(x,mod -2); } protected long pow(long x,long n){ return pow(x,n,Util.mod); } protected long pow(long x,long n,long mod){ long ret = 1; for (x %= mod;0 < n;x = x *x %mod,n >>= 1) if ((n &1) == 1) ret = ret *x %mod; return ret; } protected int bSearchI(int o,int n,IntPredicate judge){ if (!judge.test(o)) return o -Integer.signum(n -o); for (int m = 0;1 < abs(n -o);) m = judge.test(m = o +n >>1) ? (o = m) : (n = m); return o; } protected long bSearchL(long o,long n,LongPredicate judge){ for (long m = 0;1 < abs(n -o);) m = judge.test(m = o +n >>1) ? (o = m) : (n = m); return o; } protected double bSearchD(double o,double n,DoublePredicate judge){ for (double m,c = 0;c < 100;c++) m = judge.test(m = (o +n) /2) ? (o = m) : (n = m); return o; } protected long gcd(long a,long b){ while (0 < b) { long t = a; a = b; b = t %b; } return a; } public long lcm(long a,long b){ return b /gcd(a,b) *a; } protected long ceil(long a,long b){ return (a +b -1) /b; } } class Util{ public static String yes = "Yes",no = "No"; public static int infI = (1 <<30) -1; public static long infL = (1L <<61 |1 <<30) -1, mod = 998244353; public static Random rd = ThreadLocalRandom.current(); private long st = System.currentTimeMillis(); protected long elapsed(){ return System.currentTimeMillis() -st; } protected void reset(){ st = System.currentTimeMillis(); } public static int[] arrI(int N,IntUnaryOperator f){ int[] ret = new int[N]; setAll(ret,f); return ret; } public static long[] arrL(int N,IntToLongFunction f){ long[] ret = new long[N]; setAll(ret,f); return ret; } public static double[] arrD(int N,IntToDoubleFunction f){ double[] ret = new double[N]; setAll(ret,f); return ret; } public static T[] arr(T[] arr,IntFunction f){ setAll(arr,f); return arr; } public int[][] addId(int[][] T){ return arr(new int[T.length][],i -> { int[] t = copyOf(T[i],T[i].length +1); t[t.length -1] = i; return t; }); } @SuppressWarnings("unchecked") public static T cast(Object obj){ return (T) obj; } } class MyReader{ private byte[] buf = new byte[1 <<16]; private int ptr,tail; private InputStream in; public MyReader(InputStream in){ this.in = in; } private byte read(){ if (ptr == tail) try { tail = in.read(buf); ptr = 0; } catch (IOException e) {} return buf[ptr++]; } private boolean isPrintable(byte c){ return 32 < c && c < 127; } private byte nextPrintable(){ byte ret = read(); while (!isPrintable(ret)) ret = read(); return ret; } public int it(){ return toIntExact(lg()); } public int[] it(int N){ return Util.arrI(N,i -> it()); } public int[][] it(int H,int W){ return Util.arr(new int[H][],i -> it(W)); } public int idx(){ return it() -1; } public int[] idx(int N){ return Util.arrI(N,i -> idx()); } public int[][] idx(int H,int W){ return Util.arr(new int[H][],i -> idx(W)); } public long lg(){ byte i = nextPrintable(); boolean negative = i == 45; long n = negative ? 0 : i -'0'; while (isPrintable(i = read())) n = 10 *n +i -'0'; return negative ? -n : n; } public long[] lg(int N){ return Util.arrL(N,i -> lg()); } public long[][] lg(int H,int W){ return Util.arr(new long[H][],i -> lg(W)); } public double dbl(){ return Double.parseDouble(str()); } public double[] dbl(int N){ return Util.arrD(N,i -> dbl()); } public double[][] dbl(int H,int W){ return Util.arr(new double[H][],i -> dbl(W)); } public char[] ch(){ return str().toCharArray(); } public char[][] ch(int H){ return Util.arr(new char[H][],i -> ch()); } public String line(){ StringBuilder sb = new StringBuilder(); for (byte c;(c = read()) != '\n';) sb.append((char) c); return sb.toString(); } public String str(){ StringBuilder sb = new StringBuilder(); sb.append((char) nextPrintable()); for (byte c;isPrintable(c = read());) sb.append((char) c); return sb.toString(); } public String[] str(int N){ return Util.arr(new String[N],i -> str()); } public String[][] str(int H,int W){ return Util.arr(new String[H][],i -> str(W)); } } class MyWriter{ private OutputStream out; private byte[] buf = new byte[1 <<16],ibuf = new byte[20]; private int tail; private boolean autoflush; public MyWriter(OutputStream out,boolean autoflush){ this.out = out; this.autoflush = autoflush; } public void flush(){ try { out.write(buf,0,tail); tail = 0; } catch (IOException e) { e.printStackTrace(); } } private void ln(){ write((byte) '\n'); if (autoflush) flush(); } private void write(byte b){ buf[tail++] = b; if (tail == buf.length) flush(); } private void write(long n){ if (n < 0) { n = -n; write((byte) '-'); } int i = ibuf.length; do { ibuf[--i] = (byte) (n %10 +'0'); n /= 10; } while (n > 0); while (i < ibuf.length) write(ibuf[i++]); } private void print(Object obj){ if (obj instanceof Boolean) print((boolean) obj ? Util.yes : Util.no); else if (obj instanceof Integer) write((int) obj); else if (obj instanceof Long) write((long) obj); else if (obj instanceof char[]) for (char b:(char[]) obj) write((byte) b); else if (obj.getClass().isArray()) { int l = Array.getLength(obj); for (int i = 0;i < l;i++) { print(Array.get(obj,i)); if (i +1 < l) write((byte) ' '); } } else print(Objects.toString(obj).toCharArray()); } public void println(Object obj){ if (obj == null) obj = "null"; if (obj instanceof Iterable) for (Object e:(Iterable) obj) println(e); else if (obj.getClass().isArray() && Array.getLength(obj) > 0 && Array.get(obj,0).getClass().isArray()) { int l = Array.getLength(obj); for (int i = 0;i < l;i++) println(Array.get(obj,i)); } else { print(obj); ln(); } } public void printlns(Object... o){ print(o); ln(); } }