Problem: Petya recently found a game "Choose a Square". In this game, there are n points numbered from 1 to n on an infinite field. The i-th point has coordinates (x_i, y_i) and cost c_i.

You have to choose a square such that its sides are parallel to coordinate axes, the lower left and upper right corners belong to the line y = x, and all corners have integer coordinates.

The score you get is the sum of costs of the points covered by the selected square minus the length of the side of the square. Note that the length of the side can be zero.

Petya asks you to calculate the maximum possible score in the game that can be achieved by placing exactly one square.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the number of points on the field.

Each of the following n lines contains three integers x_i, y_i, c_i (0 ≤ x_i, y_i ≤ 10^9, -10^6 ≤ c_i ≤ 10^6) — coordinates of the i-th point and its cost, respectively.

Output

In the first line print the maximum score Petya can achieve.

In the second line print four integers x_1, y_1, x_2, y_2 (0 ≤ x_1, y_1, x_2, y_2 ≤ 2 ⋅ 10^9, x_1 = y_1, x_2 = y_2, x_1 ≤ x_2) separated by spaces — the coordinates of the lower left and upper right corners of the square which Petya has to select in order to achieve the maximum score.

Examples

Input


6
0 0 2
1 0 -5
1 1 3
2 3 4
1 4 -4
3 1 -1


Output


4
1 1 3 3


Input


5
3 3 0
3 3 -3
0 2 -1
3 1 3
0 0 -2


Output


0
1 1 1 1

Note

The field corresponding to the first example: <image>

Solution (in JAVA):

Solution:
//package educational.round73;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;

public class F {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		// (a,b)を含んでいると+x
		// 
		int n = ni();
		int[][] co = new int[n][];
		for(int i = 0;i < n;i++){
			co[i] = na(3);
			if(co[i][0] > co[i][1]){
				int d = co[i][0]; co[i][0] = co[i][1]; co[i][1] = d;
			}
		}
		int[] ys = new int[n];
		for(int i = 0;i < n;i++){
			ys[i] = co[i][1];
		}
		
		Arrays.sort(ys);
		ys = uniq(ys);
		
		Arrays.sort(co, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				if(a[0] != b[0])return a[0] - b[0];
				return -(a[2] - b[2]);
			}
		});
		
		int m = ys.length;
		StarrySkyTreePosL sst = new StarrySkyTreePosL(m);
		for(int i = 0;i < m;i++){
			sst.add(i, i+1, ys[i]);
		}
		
		long ans = 0;
		long x1 = 2000000000, x2 = 2000000000;
		for(int i = n-1;i >= 0;i--){
			int[] e = co[i];
			int ind = Arrays.binarySearch(ys, e[1]);
			if(ind < 0)ind = -ind-1;
			sst.add(ind, m, -e[2]);
			
			ind = Arrays.binarySearch(ys, e[0]);
			if(ind < 0)ind = -ind-1;
			
			long[] mp = sst.minpos(ind, m);
			long v = -mp[0] + e[0];
			if(v > ans){
				ans = v;
				x1 = e[0];
				x2 = ys[(int)mp[1]];
			}
		}
		out.println(ans);
		out.println(x1 + " " + x1 + " " + x2 + " " + x2);
	}
	
	
	public static class StarrySkyTreePosL {
		public int M, H, N;
		public long[] st;
		public long[] plus;
		public int[] pos;
		public long I = Long.MAX_VALUE/4; // I+plus<int
		
		public StarrySkyTreePosL(int n)
		{
			N = n;
			M = Integer.highestOneBit(Math.max(n-1, 1))<<2;
			H = M>>>1;
			st = new long[M];
			plus = new long[H];
			pos = new int[M];
			for(int i = M-1;i >= H;i--)pos[i] = i-H;
			for(int i = H-1;i >= 0;i--)propagate(i);
		}
		
		public StarrySkyTreePosL(long[] a)
		{
			N = a.length;
			M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
			H = M>>>1;
			st = new long[M];
			for(int i = 0;i < N;i++){
				st[H+i] = a[i];
			}
			plus = new long[H];
			Arrays.fill(st, H+N, M, I);
			pos = new int[M];
			for(int i = M-1;i >= H;i--)pos[i] = i-H;
			for(int i = H-1;i >= 1;i--)propagate(i);
		}
		
		private void propagate(int i)
		{
			if(st[2*i] <= st[2*i+1]){
				st[i] = st[2*i] + plus[i];
				pos[i] = pos[2*i];
			}else{
				st[i] = st[2*i+1] + plus[i];
				pos[i] = pos[2*i+1];
			}
		}
		
		public void add(int l, int r, long v){ if(l < r)add(l, r, v, 0, H, 1); }
		
		private void add(int l, int r, long v, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				if(cur >= H){
					st[cur] += v;
				}else{
					plus[cur] += v;
					propagate(cur);
				}
			}else{
				int mid = cl+cr>>>1;
				if(cl < r && l < mid){
					add(l, r, v, cl, mid, 2*cur);
				}
				if(mid < r && l < cr){
					add(l, r, v, mid, cr, 2*cur+1);
				}
				propagate(cur);
			}
		}
		
		public long min(int l, int r){ return l >= r ? I : min(l, r, 0, H, 1);}
		
		private long min(int l, int r, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				return st[cur];
			}else{
				int mid = cl+cr>>>1;
				long ret = I;
				if(cl < r && l < mid){
					ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
				}
				if(mid < r && l < cr){
					ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
				}
				return ret + plus[cur];
			}
		}
		
		public long[] minpos(int l, int r){ return l >= r ? null : minpos(l, r, 0, H, 1);}
		
		private long[] minpos(int l, int r, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				return new long[]{st[cur], pos[cur]};
			}else{
				int mid = cl+cr>>>1;
				long[] L = null, R = null;
				if(cl < r && l < mid){
					L = minpos(l, r, cl, mid, 2*cur);
				}
				if(mid < r && l < cr){
					R = minpos(l, r, mid, cr, 2*cur+1);
				}
				if(L == null && R == null)return null;
				if(L == null){
					R[0] += plus[cur];
					return R;
				}
				if(R == null){
					L[0] += plus[cur];
					return L;
				}
				if(L[0] <= R[0]){
					L[0] += plus[cur];
					return L;
				}else{
					R[0] += plus[cur];
					return R;
				}
			}
		}
		
		public void fall(int i)
		{
			if(i < H){
				if(2*i < H){
					plus[2*i] += plus[i];
					plus[2*i+1] += plus[i];
				}
				st[2*i] += plus[i];
				st[2*i+1] += plus[i];
				plus[i] = 0;
			}
		}
		
		public int firstle(int l, long v) {
			if(l >= H)return -1;
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				fall(i);
				i = i*2 + (cur>>>j&1);
			}
			while(true){
				fall(cur);
				if(st[cur] <= v){
					if(cur < H){
						cur = 2*cur;
					}else{
						return cur-H;
					}
				}else{
					cur++;
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
				}
			}
		}
		
		public int lastle(int l, long v) {
			if(l < 0)return -1;
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				fall(i);
				i = i*2 + (cur>>>j&1);
			}
			while(true){
				fall(cur);
				if(st[cur] <= v){
					if(cur < H){
						cur = 2*cur+1;
					}else{
						return cur-H;
					}
				}else{
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
					cur--;
				}
			}
		}		
		public long[] toArray() { return toArray(1, 0, H, new long[H]); }
		
		private long[] toArray(int cur, int l, int r, long[] ret)
		{
			if(r-l == 1){
				ret[cur-H] = st[cur];
			}else{
				toArray(2*cur, l, l+r>>>1, ret);
				toArray(2*cur+1, l+r>>>1, r, ret);
				for(int i = l;i < r;i++)ret[i] += plus[cur];
			}
			return ret;
		}
	}

	
	public static int[] uniq(int[] a)
	{
		int n = a.length;
		int p = 0;
		for(int i = 0;i < n;i++) {
			if(i == 0 || a[i] != a[i-1])a[p++] = a[i];
		}
		return Arrays.copyOf(a, p);
	}


	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new F().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}