Problem: After a terrifying forest fire in Berland a forest rebirth program was carried out. Due to it N rows with M trees each were planted and the rows were so neat that one could map it on a system of coordinates so that the j-th tree in the i-th row would have the coordinates of (i, j). However a terrible thing happened and the young forest caught fire. Now we must find the coordinates of the tree that will catch fire last to plan evacuation.

The burning began in K points simultaneously, which means that initially K trees started to burn. Every minute the fire gets from the burning trees to the ones that aren’t burning and that the distance from them to the nearest burning tree equals to 1.

Find the tree that will be the last to start burning. If there are several such trees, output any.

Input

The first input line contains two integers N, M (1 ≤ N, M ≤ 2000) — the size of the forest. The trees were planted in all points of the (x, y) (1 ≤ x ≤ N, 1 ≤ y ≤ M) type, x and y are integers.

The second line contains an integer K (1 ≤ K ≤ 10) — amount of trees, burning in the beginning. 

The third line contains K pairs of integers: x1, y1, x2, y2, ..., xk, yk (1 ≤ xi ≤ N, 1 ≤ yi ≤ M) — coordinates of the points from which the fire started. It is guaranteed that no two points coincide.

Output

Output a line with two space-separated integers x and y — coordinates of the tree that will be the last one to start burning. If there are several such trees, output any.

Examples

Input

3 3
1
2 2


Output

1 1


Input

3 3
1
1 1


Output

3 3


Input

3 3
2
1 1 3 3


Output

2 2

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;

	
		
		
		
		
			public class QA {
				
				static long MOD = 1000000007;
				static boolean b[], b1[], check;
				static ArrayList<Integer>[] amp, pa;
				static ArrayList<Pair>[] amp1;
				static ArrayList<Pair>[][] damp;
				static int left[],right[],end[],sum[],dist[],cnt[],start[],color[],parent[],prime[],size[];
				static int ans = 0,k;
				static int p = 0;
				static FasterScanner sc = new FasterScanner(System.in);
				//static Queue<Integer> q = new LinkedList<>();
				static BufferedWriter log;
				static HashSet<Pair> hs;
				static HashMap<Pair,Integer> hm;
				static PriorityQueue<Integer> pri[];
				static ArrayList<Integer>[] level;
				static Stack<Integer> st;
				static boolean boo[][];
				static Pair prr[];
				static long parent1[],parent2[],size1[],size2[],arr1[],SUM[],lev[], fibo[];
				static int arr[], ver[][];
				static private PrintWriter out = new PrintWriter(System.out);
				public static void main(String[] args) throws Exception {
			    	new Thread(null, new Runnable() {
						public void run() {
							try {
				soln();
						} catch (Exception e) {
								System.out.println(e);
							}
						}
					}, "1", 1 << 26).start();
					
				}
				private static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
				private static void tr(Object... o) {
					if (!oj)
						System.out.println(Arrays.deepToString(o));
				}
				static int dp[][];
				static int N,K,T,A,B;
				static long time;
				static int cost[][];
				static boolean b11[];
				static HashMap<Integer,Integer> h = new HashMap<>();
				static HashSet<Pair> chec;
				static long ans1;		static long ans2;
				static int BLOCK, MAX = 1000001;
				static double pi = Math.PI;
				static int Arr[], Brr[], pow[],  M;
				static long fact[] = new long[100000+1];
				static HashMap<Integer,Long> hm1;
				static HashSet<Integer> hs1[], hs2[];
				static String[] str2;
				static char[] ch1, ch2;
				static int[] s,f,D;
				static int tf,ts;
				static int see[][] = new int[2050][2050];
				static boolean bee[][] = new boolean[2050][2050];
				static Queue<Pair> q = new LinkedList<>();
				//static PriorityQueue<Integer> pq = new PriorityQueue<>(Collections.reverseOrder());
				public static void soln() throws IOException {
					//System.setIn(new FileInputStream("input.txt"));
					//System.setOut(new PrintStream("output.txt"));
					FasterScanner sc = new FasterScanner(new FileInputStream("input.txt"));//("C:\\Users\\Admin\\Desktop\\QAL2.txt"));
					//PrintWriter log1 = new PrintWriter("C:\\Users\\Admin\\Desktop\\input01");
					PrintWriter log = new PrintWriter("output.txt");//("C:\\Users\\Admin\\Desktop\\output00");
					//log = new BufferedWriter(new OutputStreamWriter(System.out));
					int n = sc.nextInt() , m = sc.nextInt();
					int k = sc.nextInt();
					for(int i = 1; i <= n ; i++) for(int j  =1;j<=m;j++) see[i][j]= 100000000;
					for(int i = 0; i < k; i++){
						int x = sc.nextInt(), y = sc.nextInt();
						bee[x][y] = true;
						see[x][y] = 0;
						q.add(new Pair(x,y));
					}
					while(!q.isEmpty()){
						//System.out.println(q);
						int x = q.peek().u, y = q.poll().v;
						if(x>1){
							see[x-1][y] = min(see[x][y]+1,see[x-1][y]);
							if(!bee[x-1][y]) q.add(new Pair(x-1,y));
							bee[x-1][y] = true;
						}
						if(x<n){
							see[x+1][y] = min(see[x][y]+1,see[x+1][y]);
							if(!bee[x+1][y]) q.add(new Pair(x+1,y));
							bee[x+1][y] = true;
						}
						if(y>1){
							see[x][y-1] = min(see[x][y]+1,see[x][y-1]);
							if(!bee[x][y-1]) q.add(new Pair(x,y-1));
							bee[x][y-1] = true;
						}
						if(y<m){
							see[x][y+1] = min(see[x][y]+1,see[x][y+1]);
							if(!bee[x][y+1]) q.add(new Pair(x,y+1));
							bee[x][y+1] = true;
						}
					}
					int ans = -1;
					Pair temp = null;
					for(int i = 1;i<=n;i++){
						for(int j = 1;j<=m;j++){
							if(see[i][j]>ans) {
								ans = see[i][j];
								temp = new Pair(i,j);
							}
						}
					}
					log.write(temp.u+" "+temp.v);
					log.close();
				}
				static int min(int a, int b){
					if(a>b) return b;
					return a;
				}
				private static double dfs(int cur,int prev){
					double r=0,n=0;
					for(int i : amp[cur]){
						if(i!=prev){
							r+=(1+dfs(i,cur));
							n++;
						}
					}
					if(n!=0){
						r=r/n;
					}
					return r;
				}
				static double fa1 = 0;
				static int fa = -1;
				static long nCr1(int n, int r){
					if(n<r) return 0;
					return (((fact[n] * modInverse(fact[n-r], MOD))%MOD)*modInverse(fact[r], MOD))%MOD;
				}
				static class Node{
					Node arr[] = new Node[2]; 
					int cnt[] = new int[2];
				}
				public static class Trie{
					Node root;
					public Trie(){
						root = new Node();
					}
					public void insert(String x){
						Node n = root;
						for(int i = 0;i < x.length() ;i++){
							int a1 = x.charAt(i)-'0';
							if(n.arr[a1]!=null){
								n.cnt[a1]++;
								n = n.arr[a1];
								continue;
							}
							n.arr[a1] = new Node();
							n.cnt[a1]++;
							n = n.arr[a1];
						}
					}
					public void delete(String x){
						Node n = root;
						for(int i = 0;i < x.length() ;i++){
							int a1 = x.charAt(i)-'0';
							if(n.cnt[a1]==1){
								n.arr[a1] = null;
								return;
							}
							else {
								n.cnt[a1]--;
								n = n.arr[a1];
							}
						}
					}
					public long get(String x){
						Node n = root;
						long ans = 0;
						for(int i = 0;i < x.length() ;i++){
							int a1 = '1' - x.charAt(i);
							if(n.arr[a1]!=null){
								ans += Math.pow(2, 30-i);
								n = n.arr[a1];
							}
							else n = n.arr[1-a1];
						//	System.out.println(ans);
						}
						return ans;
					}
				}
				public static class FenwickTree {
					
				    int[] array; // 1-indexed array, In this array We save cumulative information to perform efficient range queries and updates
	
				    public FenwickTree(int size) {
				        array = new int[size + 1];
				    }
				    public int rsq(int ind) {
				        assert ind > 0;
				        int sum = 0;
				        while (ind > 0) {
				            sum += array[ind];
				            //Extracting the portion up to the first significant one of the binary representation of 'ind' and decrementing ind by that number
				            ind -= ind & (-ind);
				        }
				        return sum;
				    }
				    public int rsq(int a, int b) {
				        assert b >= a && a > 0 && b > 0;
				        return rsq(b) - rsq(a - 1);
				    }
				    public void update(int ind, int value) {
				        assert ind > 0;
				        while (ind < array.length) {
				            array[ind] += value;
				            //Extracting the portion up to the first significant one of the binary representation of 'ind' and incrementing ind by that number
				            ind += ind & (-ind);
				        }
				    }
	
				    public int size() {
				        return array.length - 1;
				    }
				}
				static double power(double x, long y)
				{
				    if (y == 0)
				        return 1;
				    double p = power(x, y/2);
				    p = (p * p);
				 
				    return (y%2 == 0)? p : (x * p);
				}
				static int Dfs(int x, int val){
					b[x] = true;
					for(int p:hs2[x]){
						if(!b[p]){
							if(!hs1[x].contains(p)) val++;
							val += Dfs(p,0);
						}
					}
					return val;
				}
				static long nCr(int n, int r){
					if(n<r) return 0;
					else return (((fact[n]*modInverse(fact[r], MOD))%MOD)*modInverse(fact[n-r], MOD))%MOD;
				}
				static void dfs1(int x, int p){
					arr1[x] += lev[x];
					for(int v:amp[x]){
						if(v!=p){
							dfs1(v,x);
						}
					}
				}
				
				static void bfs(int x){
					
				}
				public static void seive(int n){
					b = new boolean[(n+1)];
					Arrays.fill(b, true);
					b[1] = true;
					for(int i = 2;i*i<=n;i++){
						if(b[i]){
							for(int p = 2*i;p<=n;p+=i){
								b[p] = false;
							}
						}
					}
					/*for(int i = 2;i<=n;i++){
						if(b[i]) prime[i] = i;
					}*/
				}
				
				static class Graph{
					int vertex;
					int weight;
					Graph(int v, int w){
						vertex = v;
						weight = w;
					}
				}
				static class Pair implements Comparable<Pair> {
					int u;
					int v;
					int ans;
					public Pair(){
						u = 0;
						v = 0;
					}
					public Pair(int u, int v) {
						this.u = u;
						this.v = v;
					}
					public int hashCode() {
						return Objects.hash();
					}
					public boolean equals(Object o) {
						Pair other = (Pair) o;
						return ((u == other.u && v == other.v && ans == other.ans));
					}
			 
					public int compareTo(Pair other) {
						//return Double.compare(ans, other.ans);
						return Long.compare(u, other.u); 
					}
					
					public String toString() {
						return "[u=" + u + ", v=" + v + "]";
					}
				}
				
				public static void buildGraph(int n){
					for(int i =0;i<n;i++){
						int x = sc.nextInt()-1, y = sc.nextInt()-1;
						amp[x].add(y);
						amp[y].add(x);
					}
				}
				
				
				public static int getParent(long x){
					while(parent[(int) x]!=x){
						parent[ (int) x] = parent[(int) parent[ (int) x]];
						x = parent[ (int) x];
					}
					return (int) x;
				}
				static long min(long a, long b, long c){
					if(a<b && a<c) return a;
					if(b<c) return b;
					return c;
				}
				/*
				
				static class Pair3{
					int x, y ,z;
					Pair3(int x, int y, int z){
						this.x = x;
						this.y = y;
						this.z = z;
					}
				}*/
				 static void KMPSearch(String pat, String txt)
				    {
				        int M = pat.length();
				        int N = txt.length();
				 
				        // create lps[] that will hold the longest
				        // prefix suffix values for pattern
				        int lps[] = new int[M];
				        int j = 0;  // index for pat[]
				 
				        // Preprocess the pattern (calculate lps[]
				        // array)
				        computeLPSArray(pat,M,lps);
				 
				        int i = 0;  // index for txt[]
				        while (i < N)
				        {
				            if (pat.charAt(j) == txt.charAt(i))
				            {
				                j++;
				                i++;
				            }
				            if (j == M)
				            {
				               // parent.add((i-j));
				                j = lps[j-1];
				            }
				 
				            // mismatch after j matches
				            else if (i < N && pat.charAt(j) != txt.charAt(i))
				            {
				                // Do not match lps[0..lps[j-1]] characters,
				                // they will match anyway
				                if (j != 0)
				                    j = lps[j-1];
				                else
				                    i = i+1;
				            }
				        }
				    }
				 static void computeLPSArray(String pat, int M, int lps[])
				    {
				        // length of the previous longest prefix suffix
				        int len = 0;
				        int i = 1;
				        lps[0] = 0;  // lps[0] is always 0
				 
				        // the loop calculates lps[i] for i = 1 to M-1
				        while (i < M)
				        {
				            if (pat.charAt(i) == pat.charAt(len))
				            {
				                len++;
				                lps[i] = len;
				                i++;
				            }
				            else  // (pat[i] != pat[len])
				            {
				                // This is tricky. Consider the example.
				                // AAACAAAA and i = 7. The idea is similar 
				                // to search step.
				                if (len != 0)
				                {
				                    len = lps[len-1];
				 
				                    // Also, note that we do not increment
				                    // i here
				                }
				                else  // if (len == 0)
				                {
				                    lps[i] = len;
				                    i++;
				                }
				            }
				        }
				    }
				private static void permutation(String prefix, String str) {
				    int n = str.length();
				    if (n == 0); //hs.add(prefix);
				    else {
				        for (int i = 0; i < n; i++)
				            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
				    }
				}
				
				public static void buildTree(int n){
					int arr[] = sc.nextIntArray(n);
					for(int i = 0;i<n;i++){
						int x = arr[i]-1;
						amp[i+1].add(x);
						amp[x].add(i+1);
					}
				}
				
				static class SegmentTree {
					boolean st[];
					boolean lazy[];
		
					SegmentTree(int n) {
						int size = 4 * n;
						st = new boolean[size];
						Arrays.fill(st, true);
						lazy = new boolean[size];
						Arrays.fill(lazy, true);
						//build(0, n - 1, 1);
					}
					
					/*long[] build(int ss, int se, int si) {
						if (ss == se) {
							st[si][0] = 1;
							st[si][1] = 1;
							st[si][2] = 1;
							return st[si];
						}
						int mid = (ss + se) / 2;
						long a1[] = build(ss, mid, si * 2), a2[] = build(mid + 1, se,
								si * 2 + 1);
						long ans[] = new long[3];
						if (arr[mid] < arr[mid + 1]) {
							ans[1] = Math.max(a2[1], Math.max(a1[1], a1[2] + a2[0]));
							if (a1[1] == (mid - ss + 1))
								ans[0] = ans[1];
							else
								ans[0] = a1[0];
							if (a2[2] == (se - mid))
								ans[2] = ans[1];
							else
								ans[2] = a2[2];
						} else {
							ans[1] = Math.max(a1[1], a2[1]);
							ans[0] = a1[0];
							ans[2] = a2[2];
						}
						st[si] = ans;
						return st[si];
					}*/
		
					void update(int si, int ss, int se, int idx, long x) {
						if (ss == se) {
							//arr[idx] += val;
							st[si]=false;
						} 
						else {
							int mid = (ss + se) / 2;
							if(ss <= idx && idx <= mid)
					        {
					             update(2*si, ss, mid, idx, x);
					        }
					        else
					        { update(2*si+1, mid+1, se, idx, x);
					        }
							st[si] = st[2*si]|st[2*si+1];
						}
					}
					/*boolean get(int qs, int qe, int ss, int se, int si){
						if(qs>se || qe<ss) return 0;
						if (qs <= ss && qe >= se) {
							return st[si];
						}
						int mid = (ss+se)/2;
						return get(qs, qe, ss, mid, si * 2)+get(qs, qe, mid + 1, se, si * 2 + 1);
					}*/
					void updateRange(int node, int start, int end, int l, int r, boolean val)
					{
					    if(!lazy[node])
					    { 
					        // This node needs to be updated
					        st[node] = lazy[node];    // Update it
					        if(start != end)
					        {
					            lazy[node*2] = lazy[node];                  // Mark child as lazy
					            lazy[node*2+1] = lazy[node];                // Mark child as lazy
					        }
					        lazy[node] = true;                                  // Reset it
					    }
					    if(start > end || start > r || end < l)              // Current segment is not within range [l, r]
					        return;
					    if(start >= l && end <= r)
					    {
					        // Segment is fully within range
					        st[node] =  val;
					        if(start != end)
					        {
					            // Not leaf node
					            lazy[node*2] = val;
					            lazy[node*2+1] = val;
					        }
					        return;
					    }
					    int mid = (start + end) / 2;
					    updateRange(node*2, start, mid, l, r, val);        // Updating left child
					    updateRange(node*2 + 1, mid + 1, end, l, r, val);   // Updating right child
					    st[node] = st[node*2] | st[node*2+1];        // Updating root with max value 
					}
		
					boolean queryRange(int node, int start, int end, int l, int r)
					{
					    if(start > end || start > r || end < l)
					        return false;         // Out of range
					    if(!lazy[node])
					    {
					        // This node needs to be updated
					        st[node] = lazy[node];            // Update it
					        if(start != end)
					        {
					            lazy[node*2] = lazy[node];         // Mark child as lazy
					            lazy[node*2+1] = lazy[node];    // Mark child as lazy
					        }
					        lazy[node] = true;                 // Reset it
					    }
					    if(start >= l && end <= r)             // Current segment is totally within range [l, r]
					        return  st[node];
					    int mid = (start + end) / 2;
					    boolean p1 = queryRange(node*2, start, mid, l, r);         // Query left child
					    boolean b = queryRange(node*2 + 1, mid + 1, end, l, r); // Query right child
					    return (p1 | b);
					}
					void print() {
						for (int i = 0; i < st.length; i++) {
							System.out.print(st[i]+" ");
						}
						System.out.println();
					}
				}
				static int convert(int x){
					int cnt = 0;
					String str = Integer.toBinaryString(x);
					//System.out.println(str);
					for(int i = 0;i<str.length();i++){
						if(str.charAt(i)=='1'){
							cnt++;
						}
					}
					int ans = (int) Math.pow(3, 6-cnt);
					return ans;
				}
				static class Node2{
					Node2 left = null;
					Node2 right = null;
					Node2 parent = null;
					int data;
				}
				static boolean check(char ch[][], int i, int j){
					if(ch[i][j]=='O') return false;
					char c = ch[i][j];
					ch[i][j] = 'X';
					if(c=='X'){
					if(i>=4){
						int x = 0;
						int l = 0;
						for(x = 0;x<=4;x++){
							if(ch[i-x][j]!='X'){ if(ch[i-x][j]!='.') break;else l++;}
						}
						if(x==5 && l<=1) return true;
						l = 0;
						if(j>=4){
							for(x = 0;x<=4;x++){
								if(ch[i-x][j-x]!='X'){ if(ch[i-x][j-x]!='.') break; else l++;}
							}
							if(x==5 && l<=1) return true;
							 l =0;
							for(x = 0;x<=4;x++){
								if(ch[i][j-x]!='X'){ if(ch[i][j-x]!='.') break; else l++;}
							}
							if(x==5 && l<=1) return true;
						}
						if(j<=5){
							l = 0;
							for(x = 0;x<=4;x++){
								if(ch[i][j+x]!='X'){ if(ch[i][j+x]!='.') break; else l++;}
							}
							if(x==5 && l<=1) return true;
							l = 0;
							for(x = 0;x<=4;x++){
								if(ch[i-x][j+x]!='X'){ if(ch[i-x][j+x]!='.') break; else l++;}
							}
							if(x==5 && l<=1) return true;
						}
					}
					if(i<=5){
						int x = 0;
						int l = 0;
						for(x = 0;x<=4;x++){
							if(ch[i+x][j]!='X'){ if(ch[i+x][j]!='.') break; else l++;}
						}
						if(x==5 && l<=1) return true;
						l = 0;
						if(j>=4){
							for(x = 0;x<=4;x++){
								if(ch[i+x][j-x]!='X'){ if(ch[i+x][j-x]!='.') break; else l++;}
							}
							if(x==5 && l<=1) return true;
							 l =0;
							for(x = 0;x<=4;x++){
								if(ch[i][j-x]!='X'){ if(ch[i][j-x]!='.') break; else l++;}
							}
							if(x==5 && l<=1) return true;
						}
						if(j<=5){
							l = 0;
							for(x = 0;x<=4;x++){
								if(ch[i][j+x]!='X'){ if(ch[i][j+x]!='.') break; else l++;}
							}
							if(x==5 && l<=1) return true;
							l = 0;
							for(x = 0;x<=4;x++){
								if(ch[i+x][j+x]!='X'){ if(ch[i+x][j+x]!='.') break; else l++;}
							}
							if(x==5 && l<=1) return true;
						}
					}
					}
					else{
						if(i>=4){
							int x = 0;
							int l = 0;
							for(x = 0;x<=4;x++){
								if(ch[i-x][j]!='X'){ if(ch[i-x][j]!='.') break;else l++;}
							}
							if(x==5 && l<=0) return true;
							l = 0;
							if(j>=4){
								for(x = 0;x<=4;x++){
									if(ch[i-x][j-x]!='X'){ if(ch[i-x][j-x]!='.') break; else l++;}
								}
								if(x==5 && l<=0) return true;
								 l =0;
								for(x = 0;x<=4;x++){
									if(ch[i][j-x]!='X'){ if(ch[i][j-x]!='.') break; else l++;}
								}
								if(x==5 && l<=0) return true;
							}
							if(j<=5){
								l = 0;
								for(x = 0;x<=4;x++){
									if(ch[i][j+x]!='X'){ if(ch[i][j+x]!='.') break; else l++;}
								}
								if(x==5 && l<=0) return true;
								l = 0;
								for(x = 0;x<=4;x++){
									if(ch[i-x][j+x]!='X'){ if(ch[i-x][j+x]!='.') break; else l++;}
								}
								if(x==5 && l<=0) return true;
							}
						}
						if(i<=5){
							int x = 0;
							int l = 0;
							for(x = 0;x<=4;x++){
								if(ch[i+x][j]!='X'){ if(ch[i+x][j]!='.') break; else l++;}
							}
							if(x==5 && l<=0) return true;
							l = 0;
							if(j>=4){
								for(x = 0;x<=4;x++){
									if(ch[i+x][j-x]!='X'){ if(ch[i+x][j-x]!='.') break; else l++;}
								}
								if(x==5 && l<=0) return true;
								 l =0;
								for(x = 0;x<=4;x++){
									if(ch[i][j-x]!='X'){ if(ch[i][j-x]!='.') break; else l++;}
								}
								if(x==5 && l<=0) return true;
							}
							if(j<=5){
								l = 0;
								for(x = 0;x<=4;x++){
									if(ch[i][j+x]!='X'){ if(ch[i][j+x]!='.') break; else l++;}
								}
								if(x==5 && l<=0) return true;
								l = 0;
								for(x = 0;x<=4;x++){
									if(ch[i+x][j+x]!='X'){ if(ch[i+x][j+x]!='.') break; else l++;}
								}
								if(x==5 && l<=0) return true;
							}
						}
					}
					ch[i][j] = c;
					
					return false;
				}
				static class BinarySearchTree{
					Node2 root = null;
					int height = 0;
					int max = 0;
					int cnt = 1;
					ArrayList<Integer> parent = new ArrayList<>();
					HashMap<Integer, Integer> hm = new HashMap<>();
					public void insert(int x){
						Node2 n = new Node2();
						n.data = x;
						if(root==null){
							root = n;
						}
						else{
							Node2 temp = root,temb = null;
							while(temp!=null){
								temb = temp;
								if(x>temp.data) temp = temp.right;
								else temp = temp.left;
							}
							if(x>temb.data) temb.right = n;
							else temb.left = n;
							n.parent = temb;
							parent.add(temb.data);
						}
					}
					public Node2 getSomething(int x, int y, Node2 n){
						if(n.data==x || n.data==y) return n;
						else if(n.data>x && n.data<y) return n;
						else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
						else return getSomething(x,y,n.left);
					}
					public Node2 search(int x,Node2 n){
						if(x==n.data){
							max = Math.max(max, n.data);
							return n;
						}
						if(x>n.data){
							max = Math.max(max, n.data);
							return search(x,n.right);
						}
						else{
							max = Math.max(max, n.data);
							return search(x,n.left);
						}
					}
					public int getHeight(Node2 n){
						if(n==null) return 0;
						height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
						return height;
					}
				}
				static long findDiff(long[] arr, long[] brr, int m){
					int i = 0, j = 0;
					long fa = 1000000000000L;
					while(i<m && j<m){
						long x = arr[i]-brr[j];
						if(x>=0){
							if(x<fa) fa = x;
							j++;
						}
						else{
							if((-x)<fa) fa = -x;
							i++;
						}
					}
					return fa;
				}
				public static long max(long x, long y, long z){
					if(x>=y && x>=z) return x;
					if(y>=x && y>=z) return y;
					return z;
				}
				
				static long modInverse(long a, long mOD2){
				            return  power(a, mOD2-2, mOD2);
				}
				static long power(long x, long y, long m)
				{
				    if (y == 0)
				        return 1;
				    long p = power(x, y/2, m) % m;
				    p = (p * p) % m;
				 
				    return (y%2 == 0)? p : (x * p) % m;
				}
				static long d,x,y;
				public static void extendedEuclidian(long a, long b){
					if(b == 0) {
				        d = a;
				        x = 1;
				        y = 0;
				    }
				    else {
				        extendedEuclidian(b, a%b);
				        int temp = (int) x;
				        x = y;
				        y = temp - (a/b)*y;
				    }
				}
				
				public static long gcd(long n, long m){
					if(m!=0) return gcd(m,n%m);
					else return n;
				}
				
				static BufferedReader reader;
			    static StringTokenizer tokenizer;
			    static PrintWriter writer;
			
			
			   
			    static class FasterScanner {
		
					private final InputStream stream;
					private final byte[] buf = new byte[8192];
					private int curChar, snumChars;
					private SpaceCharFilter filter;
		
					public FasterScanner(InputStream stream) {
						this.stream = stream;
					}
		
					public int snext() {
						if (snumChars == -1)
							throw new InputMismatchException();
						if (curChar >= snumChars) {
							curChar = 0;
							try {
								snumChars = stream.read(buf);
							} catch (IOException e) {
								throw new InputMismatchException();
							}
							if (snumChars <= 0)
								return -1;
						}
						return buf[curChar++];
					}
		
					public int nextInt() {
						int c = snext();
						while (isSpaceChar(c)) {
							c = snext();
						}
						int sgn = 1;
						if (c == '-') {
							sgn = -1;
							c = snext();
						}
						int res = 0;
						do {
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = snext();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
		
					public long nextLong() {
						int c = snext();
						while (isSpaceChar(c)) {
							c = snext();
						}
						int sgn = 1;
						if (c == '-') {
							sgn = -1;
							c = snext();
						}
						long res = 0;
						do {
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = snext();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
		
					public int[] nextIntArray(int n) {
						int a[] = new int[n];
						for (int i = 0; i < n; i++) {
							a[i] = nextInt();
						}
						return a;
					}
		
					public long[] nextLongArray(int n) {
						long a[] = new long[n];
						for (int i = 0; i < n; i++) {
							a[i] = nextLong();
						}
						return a;
					}
			                
					public String readString() {
						int c = snext();
						while (isSpaceChar(c)) {
							c = snext();
						}
						StringBuilder res = new StringBuilder();
						do {
							res.appendCodePoint(c);
							c = snext();
						} while (!isSpaceChar(c));
						return res.toString();
					}
		
					public String nextLine() {
						int c = snext();
						while (isSpaceChar(c))
							c = snext();
						StringBuilder res = new StringBuilder();
						do {
							res.appendCodePoint(c);
							c = snext();
						} while (!isEndOfLine(c));
						return res.toString();
					}
		
					public boolean isSpaceChar(int c) {
						if (filter != null)
							return filter.isSpaceChar(c);
						return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
					}
		
					private boolean isEndOfLine(int c) {
						return c == '\n' || c == '\r' || c == -1;
					}
		
					public interface SpaceCharFilter {
						public boolean isSpaceChar(int ch);
					}
				}
			}