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 com.company;

import java.io.*;
import java.util.*;

public class Main {
    public static class Task {

        public class SegmentTree {
            long[] nodeSum;
            long[] nodePrefixMaxSum;
            int[] nodePrefixMaxSumIndex;
            int n;
            int baseVal;
            public SegmentTree(int n) {
                this.n = 1;
                this.baseVal = 1;
                while (this.baseVal < n) this.baseVal *= 2;
                nodeSum = new long[this.baseVal * 2];
                nodePrefixMaxSum = new long[this.baseVal * 2];
                nodePrefixMaxSumIndex = new int[this.baseVal * 2];
                for (int i = 0; i < n; i++) {
                    nodePrefixMaxSumIndex[i + baseVal] = i + 1;
                }
            }

            public void modify(int index, long val) {
                index += this.baseVal;
                nodeSum[index] += val;
                nodePrefixMaxSum[index] += val;
                while (index != 1) {
                    index /= 2;
                    int leftChild = index << 1;
                    int rightChild = index << 1 | 1;
                    nodeSum[index] = nodeSum[leftChild] + nodeSum[rightChild];
                    if (nodePrefixMaxSum[leftChild] < nodeSum[leftChild] + nodePrefixMaxSum[rightChild]) {
                        nodePrefixMaxSum[index] = nodeSum[leftChild] + nodePrefixMaxSum[rightChild];
                        nodePrefixMaxSumIndex[index] = nodePrefixMaxSumIndex[rightChild];
                    } else {
                        nodePrefixMaxSum[index] = nodePrefixMaxSum[leftChild];
                        nodePrefixMaxSumIndex[index] = nodePrefixMaxSumIndex[leftChild];
                    }
                }
            }

            public long[] getMaxPrefixSum(int index) { // return {index, value}
                index += baseVal;
                long bestPrefixSum = nodePrefixMaxSum[index];
                long bestPrefixIndex = nodePrefixMaxSumIndex[index];
                while (index != 1) {
                    int parent = index / 2;
                    int leftChild = parent << 1;
                    int rightChild = parent << 1 | 1;
                    if (leftChild == index) {
                        if (nodeSum[leftChild] + nodePrefixMaxSum[rightChild] > bestPrefixSum) {
                            bestPrefixSum = nodeSum[leftChild] + nodePrefixMaxSum[rightChild];
                            bestPrefixIndex = nodePrefixMaxSumIndex[rightChild];
                        }
                    }
                    index = parent;
                }
                return new long[]{bestPrefixIndex, bestPrefixSum};
            }
        }

        public void solve(Scanner sc, PrintWriter pw) throws IOException {
            int n = sc.nextInt();
            int[][] segs = new int[n][3];
            Set<Integer> diff = new HashSet<>();
            for (int i = 0; i < n; i++) {
                int x = sc.nextInt();
                int y = sc.nextInt();
                int c = sc.nextInt();
                segs[i][0] = Math.min(x, y);
                segs[i][1] = Math.max(x, y);
                segs[i][2] = c;
                diff.add(x);
                diff.add(y);
            }
            List<Integer> arrDiff = new ArrayList<>(diff);
            Collections.sort(arrDiff);
            Map<Integer, Integer> actualCoordinateToVirtual = new HashMap<>();
            int[] virtualCoordinateNextSpace = new int[arrDiff.size() - 1];
            for (int i = 0; i < arrDiff.size(); i++) {
                actualCoordinateToVirtual.put(arrDiff.get(i), i);
                if (i < arrDiff.size() - 1) virtualCoordinateNextSpace[i] = arrDiff.get(i + 1) - arrDiff.get(i);
            }
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < 2; j++) {
                    segs[i][j] = actualCoordinateToVirtual.get(segs[i][j]);
                }
            }

            SegmentTree st = new SegmentTree(arrDiff.size());
            for (int i = 0; i < arrDiff.size() - 1; i++) {
                st.modify(i + 1, -virtualCoordinateNextSpace[i]);
            }
            for (int i = 0; i < segs.length; i++) {
                st.modify(segs[i][1], segs[i][2]);
            }
            Arrays.sort(segs, new Comparator<int[]>() {
                @Override
                public int compare(int[] t1, int[] t2) {
                    return t1[0] - t2[0];
                }
            });
            int sIdx = 0;
            long maxSol = 0;
            int bestStart = 1_000_000_001, bestEnd = 1_000_000_001;
            for (int i = 0; i < arrDiff.size(); i++) {
                long[] query = st.getMaxPrefixSum(i);
                int rightIndex = (int) query[0];
                long sum = query[1];
                if (sum > maxSol) {
                    maxSol = sum;
                    bestStart = arrDiff.get(i);
                    bestEnd = arrDiff.get(rightIndex - 1);
                }
                while (sIdx < n && segs[sIdx][0] == i) {
                    st.modify(segs[sIdx][1], -segs[sIdx][2]);
                    sIdx++;
                }
                if (i < arrDiff.size() - 1)
                    st.modify(i + 1, virtualCoordinateNextSpace[i]);
            }
            System.out.println(maxSol);
            System.out.print(bestStart + " ");
            System.out.print(bestStart + " ");
            System.out.print(bestEnd + " ");
            System.out.println(bestEnd);
        }
    }

    // template, actual code is in class Task.
    static long TIME_START, TIME_END;

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
//        Scanner sc = new Scanner(new FileInputStream("Test.in"));
        PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));
//        PrintWriter pw = new PrintWriter(new FileOutputStream("Test.out"));

        Runtime runtime = Runtime.getRuntime();
        long usedMemoryBefore = runtime.totalMemory() - runtime.freeMemory();
        TIME_START = System.currentTimeMillis();
        Task t = new Task();
        t.solve(sc, pw);
        TIME_END = System.currentTimeMillis();
        long usedMemoryAfter = runtime.totalMemory() - runtime.freeMemory();
        pw.close();
//        System.err.println("Memory increased: " + (usedMemoryAfter - usedMemoryBefore) / 1000000);
//        System.err.println("Time used: " + (TIME_END - TIME_START) + ".");
    }

    // Faster IO with BufferedReader wrapped with Scanner
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader s) throws FileNotFoundException {
            br = new BufferedReader(s);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}