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:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author aryssoncf
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        FChooseASquare solver = new FChooseASquare();
        solver.solve(1, in, out);
        out.close();
    }

    static class FChooseASquare {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            int[] X = new int[n], Y = new int[n], C = new int[n];
            in.readIntArrays(X, Y, C);
            for (int i = 0; i < n; i++) {
                if (X[i] > Y[i]) {
                    int tmp = X[i];
                    X[i] = Y[i];
                    Y[i] = tmp;
                }
            }
            int[] orig = ArrayUtils.compress(X, Y);
            int m = orig.length;
            long[] neg = new long[m];
            Arrays.setAll(neg, i -> -(long) orig[i] * m + i);
            int[] order = ArrayUtils.order(X);
            int idx = 0;
            IntervalTree it = new ArrayBasedIntervalTree(neg) {

                protected long joinValue(long left, long right) {
                    return Math.max(left, right);
                }


                protected long joinDelta(long was, long delta) {
                    return was + delta;
                }


                protected long accumulate(long value, long delta, int length) {
                    return value + delta;
                }


                protected long neutralValue() {
                    return Long.MIN_VALUE;
                }


                protected long neutralDelta() {
                    return 0;
                }
            };
            for (int i = 0; i < n; i++) {
                it.update(Y[i], m - 1, (long) C[i] * m);
            }
            long res = 0;
            int from = orig[m - 1] + 1, to = orig[m - 1] + 1;
            for (int i = 0; i < m; i++) {
                it.update(i, m - 1, (long) (orig[i] - (i == 0 ? 0 : orig[i - 1])) * m);
                while (idx < n && X[order[idx]] < i) {
                    int id = order[idx], pos = Y[id], val = C[id];
                    idx++;
                    it.update(pos, m - 1, -(long) val * m);
                }
                long q = it.query(i, m - 1);
                if (q > res) {
                    res = q;
                    from = orig[i];
                    int pos = (int) (q % m);
                    to = orig[pos];
                }
            }
            res /= m;
            out.printLine(res);
            out.printLine(from, from, to, to);
        }

    }

    static class IntArrayList extends IntAbstractStream implements IntList {
        private int size;
        private int[] data;

        public IntArrayList() {
            this(3);
        }

        public IntArrayList(int capacity) {
            data = new int[capacity];
        }

        public IntArrayList(IntCollection c) {
            this(c.size());
            addAll(c);
        }

        public IntArrayList(IntStream c) {
            this();
            if (c instanceof IntCollection) {
                ensureCapacity(((IntCollection) c).size());
            }
            addAll(c);
        }

        public IntArrayList(IntArrayList c) {
            size = c.size();
            data = c.data.clone();
        }

        public IntArrayList(int[] arr) {
            size = arr.length;
            data = arr.clone();
        }

        public int size() {
            return size;
        }

        public int get(int at) {
            if (at >= size) {
                throw new IndexOutOfBoundsException("at = " + at + ", size = " + size);
            }
            return data[at];
        }

        private void ensureCapacity(int capacity) {
            if (data.length >= capacity) {
                return;
            }
            capacity = Math.max(2 * data.length, capacity);
            data = Arrays.copyOf(data, capacity);
        }

        public void addAt(int index, int value) {
            ensureCapacity(size + 1);
            if (index > size || index < 0) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != size) {
                System.arraycopy(data, index, data, index + 1, size - index);
            }
            data[index] = value;
            size++;
        }

        public void removeAt(int index) {
            if (index >= size || index < 0) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != size - 1) {
                System.arraycopy(data, index + 1, data, index, size - index - 1);
            }
            size--;
        }

        public void set(int index, int value) {
            if (index >= size) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            data[index] = value;
        }

        public int[] toArray() {
            return Arrays.copyOf(data, size);
        }

    }

    static interface IntReversableCollection extends IntCollection {
    }

    static class Sorter {
        private static final int INSERTION_THRESHOLD = 16;

        private Sorter() {
        }

        public static void sort(IntList list, IntComparator comparator) {
            quickSort(list, 0, list.size() - 1, (Integer.bitCount(Integer.highestOneBit(list.size()) - 1) * 5) >> 1,
                    comparator);
        }

        private static void quickSort(IntList list, int from, int to, int remaining, IntComparator comparator) {
            if (to - from < INSERTION_THRESHOLD) {
                insertionSort(list, from, to, comparator);
                return;
            }
            if (remaining == 0) {
                heapSort(list, from, to, comparator);
                return;
            }
            remaining--;
            int pivotIndex = (from + to) >> 1;
            int pivot = list.get(pivotIndex);
            list.swap(pivotIndex, to);
            int storeIndex = from;
            int equalIndex = to;
            for (int i = from; i < equalIndex; i++) {
                int value = comparator.compare(list.get(i), pivot);
                if (value < 0) {
                    list.swap(storeIndex++, i);
                } else if (value == 0) {
                    list.swap(--equalIndex, i--);
                }
            }
            quickSort(list, from, storeIndex - 1, remaining, comparator);
            for (int i = equalIndex; i <= to; i++) {
                list.swap(storeIndex++, i);
            }
            quickSort(list, storeIndex, to, remaining, comparator);
        }

        private static void heapSort(IntList list, int from, int to, IntComparator comparator) {
            for (int i = (to + from - 1) >> 1; i >= from; i--) {
                siftDown(list, i, to, comparator, from);
            }
            for (int i = to; i > from; i--) {
                list.swap(from, i);
                siftDown(list, from, i - 1, comparator, from);
            }
        }

        private static void siftDown(IntList list, int start, int end, IntComparator comparator, int delta) {
            int value = list.get(start);
            while (true) {
                int child = ((start - delta) << 1) + 1 + delta;
                if (child > end) {
                    return;
                }
                int childValue = list.get(child);
                if (child + 1 <= end) {
                    int otherValue = list.get(child + 1);
                    if (comparator.compare(otherValue, childValue) > 0) {
                        child++;
                        childValue = otherValue;
                    }
                }
                if (comparator.compare(value, childValue) >= 0) {
                    return;
                }
                list.swap(start, child);
                start = child;
            }
        }

        private static void insertionSort(IntList list, int from, int to, IntComparator comparator) {
            for (int i = from + 1; i <= to; i++) {
                int value = list.get(i);
                for (int j = i - 1; j >= from; j--) {
                    if (comparator.compare(list.get(j), value) <= 0) {
                        break;
                    }
                    list.swap(j, j + 1);
                }
            }
        }

    }

    static class IntArray extends IntAbstractStream implements IntList {
        private int[] data;

        public IntArray(int[] arr) {
            data = arr;
        }

        public int size() {
            return data.length;
        }

        public int get(int at) {
            return data[at];
        }

        public void addAt(int index, int value) {
            throw new UnsupportedOperationException();
        }

        public void removeAt(int index) {
            throw new UnsupportedOperationException();
        }

        public void set(int index, int value) {
            data[index] = value;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

    }

    static class Range {
        public static IntList range(int from, int to) {
            int[] result = new int[Math.abs(from - to)];
            int current = from;
            if (from <= to) {
                for (int i = 0; i < result.length; i++) {
                    result[i] = current++;
                }
            } else {
                for (int i = 0; i < result.length; i++) {
                    result[i] = current--;
                }
            }
            return new IntArray(result);
        }

    }

    static interface IntCollection extends IntStream {
        public int size();

        default public void add(int value) {
            throw new UnsupportedOperationException();
        }

        default public int[] toArray() {
            int size = size();
            int[] array = new int[size];
            int i = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                array[i++] = it.value();
            }
            return array;
        }

        default public IntCollection addAll(IntStream values) {
            for (IntIterator it = values.intIterator(); it.isValid(); it.advance()) {
                add(it.value());
            }
            return this;
        }

    }

    static abstract class ArrayBasedIntervalTree extends LongIntervalTree {
        private long[] array;

        protected ArrayBasedIntervalTree(long[] array) {
            super(array.length, false);
            this.array = array;
            init();
        }

        protected long initValue(int index) {
            return array[index];
        }

    }

    static abstract class LongIntervalTree extends IntervalTree {
        protected long[] value;
        protected long[] delta;

        protected LongIntervalTree(int size) {
            this(size, true);
        }

        public LongIntervalTree(int size, boolean shouldInit) {
            super(size, shouldInit);
        }

        protected void initData(int size, int nodeCount) {
            value = new long[nodeCount];
            delta = new long[nodeCount];
        }

        protected abstract long joinValue(long left, long right);

        protected abstract long joinDelta(long was, long delta);

        protected abstract long accumulate(long value, long delta, int length);

        protected abstract long neutralValue();

        protected abstract long neutralDelta();

        protected long initValue(int index) {
            return neutralValue();
        }

        protected void initAfter(int root, int left, int right, int middle) {
            value[root] = joinValue(value[2 * root + 1], value[2 * root + 2]);
            delta[root] = neutralDelta();
        }

        protected void initBefore(int root, int left, int right, int middle) {
        }

        protected void initLeaf(int root, int index) {
            value[root] = initValue(index);
            delta[root] = neutralDelta();
        }

        protected void updatePostProcess(int root, int left, int right, int from, int to, long delta, int middle) {
            value[root] = joinValue(value[2 * root + 1], value[2 * root + 2]);
        }

        protected void updatePreProcess(int root, int left, int right, int from, int to, long delta, int middle) {
            pushDown(root, left, middle, right);
        }

        protected void pushDown(int root, int left, int middle, int right) {
            value[2 * root + 1] = accumulate(value[2 * root + 1], delta[root], middle - left + 1);
            value[2 * root + 2] = accumulate(value[2 * root + 2], delta[root], right - middle);
            delta[2 * root + 1] = joinDelta(delta[2 * root + 1], delta[root]);
            delta[2 * root + 2] = joinDelta(delta[2 * root + 2], delta[root]);
            delta[root] = neutralDelta();
        }

        protected void updateFull(int root, int left, int right, int from, int to, long delta) {
            value[root] = accumulate(value[root], delta, right - left + 1);
            this.delta[root] = joinDelta(this.delta[root], delta);
        }

        protected long queryPostProcess(int root, int left, int right, int from, int to, int middle, long leftResult,
                                        long rightResult) {
            return joinValue(leftResult, rightResult);
        }

        protected void queryPreProcess(int root, int left, int right, int from, int to, int middle) {
            pushDown(root, left, middle, right);
        }

        protected long queryFull(int root, int left, int right, int from, int to) {
            return value[root];
        }

        protected long emptySegmentResult() {
            return neutralValue();
        }

    }

    static abstract class IntAbstractStream implements IntStream {
        public String toString() {
            StringBuilder builder = new StringBuilder();
            boolean first = true;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                if (first) {
                    first = false;
                } else {
                    builder.append(' ');
                }
                builder.append(it.value());
            }
            return builder.toString();
        }

        public boolean equals(Object o) {
            if (!(o instanceof IntStream)) {
                return false;
            }
            IntStream c = (IntStream) o;
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                if (it.value() != jt.value()) {
                    return false;
                }
                it.advance();
                jt.advance();
            }
            return !it.isValid() && !jt.isValid();
        }

        public int hashCode() {
            int result = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                result *= 31;
                result += it.value();
            }
            return result;
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public void readIntArrays(int[]... arrays) {
            for (int i = 0; i < arrays[0].length; i++) {
                for (int j = 0; j < arrays.length; j++) {
                    arrays[j][i] = readInt();
                }
            }
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            boolean isSpaceChar(int ch);

        }

    }

    static interface IntList extends IntReversableCollection {
        public abstract int get(int index);

        public abstract void set(int index, int value);

        public abstract void addAt(int index, int value);

        public abstract void removeAt(int index);

        default public void swap(int first, int second) {
            if (first == second) {
                return;
            }
            int temp = get(first);
            set(first, get(second));
            set(second, temp);
        }

        default public IntIterator intIterator() {
            return new IntIterator() {
                private int at;
                private boolean removed;

                public int value() {
                    if (removed) {
                        throw new IllegalStateException();
                    }
                    return get(at);
                }

                public boolean advance() {
                    at++;
                    removed = false;
                    return isValid();
                }

                public boolean isValid() {
                    return !removed && at < size();
                }

                public void remove() {
                    removeAt(at);
                    at--;
                    removed = true;
                }
            };
        }

        default public void add(int value) {
            addAt(size(), value);
        }

        default public IntList sort(IntComparator comparator) {
            Sorter.sort(this, comparator);
            return this;
        }

        default IntList unique() {
            int last = Integer.MIN_VALUE;
            IntList result = new IntArrayList();
            int size = size();
            for (int i = 0; i < size; i++) {
                int current = get(i);
                if (current != last) {
                    result.add(current);
                    last = current;
                }
            }
            return result;
        }

        default public IntList subList(final int from, final int to) {
            return new IntList() {
                private final int shift;
                private final int size;

                {
                    if (from < 0 || from > to || to > IntList.this.size()) {
                        throw new IndexOutOfBoundsException("from = " + from + ", to = " + to + ", size = " + size());
                    }
                    shift = from;
                    size = to - from;
                }

                public int size() {
                    return size;
                }

                public int get(int at) {
                    if (at < 0 || at >= size) {
                        throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
                    }
                    return IntList.this.get(at + shift);
                }

                public void addAt(int index, int value) {
                    throw new UnsupportedOperationException();
                }

                public void removeAt(int index) {
                    throw new UnsupportedOperationException();
                }

                public void set(int at, int value) {
                    if (at < 0 || at >= size) {
                        throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
                    }
                    IntList.this.set(at + shift, value);
                }

                public IntList compute() {
                    return new IntArrayList(this);
                }
            };
        }

    }

    static interface IntIterator {
        public int value() throws NoSuchElementException;

        public boolean advance();

        public boolean isValid();

    }

    static abstract class IntervalTree {
        protected int size;

        protected IntervalTree(int size) {
            this(size, true);
        }

        public IntervalTree(int size, boolean shouldInit) {
            this.size = size;
            int nodeCount = Math.max(1, Integer.highestOneBit(size) << 2);
            initData(size, nodeCount);
            if (shouldInit) {
                init();
            }
        }

        protected abstract void initData(int size, int nodeCount);

        protected abstract void initAfter(int root, int left, int right, int middle);

        protected abstract void initBefore(int root, int left, int right, int middle);

        protected abstract void initLeaf(int root, int index);

        protected abstract void updatePostProcess(int root, int left, int right, int from, int to, long delta, int middle);

        protected abstract void updatePreProcess(int root, int left, int right, int from, int to, long delta, int middle);

        protected abstract void updateFull(int root, int left, int right, int from, int to, long delta);

        protected abstract long queryPostProcess(int root, int left, int right, int from, int to, int middle,
                                                 long leftResult, long rightResult);

        protected abstract void queryPreProcess(int root, int left, int right, int from, int to, int middle);

        protected abstract long queryFull(int root, int left, int right, int from, int to);

        protected abstract long emptySegmentResult();

        public void init() {
            if (size == 0) {
                return;
            }
            init(0, 0, size - 1);
        }

        private void init(int root, int left, int right) {
            if (left == right) {
                initLeaf(root, left);
            } else {
                int middle = (left + right) >> 1;
                initBefore(root, left, right, middle);
                init(2 * root + 1, left, middle);
                init(2 * root + 2, middle + 1, right);
                initAfter(root, left, right, middle);
            }
        }

        public void update(int from, int to, long delta) {
            update(0, 0, size - 1, from, to, delta);
        }

        protected void update(int root, int left, int right, int from, int to, long delta) {
            if (left > to || right < from) {
                return;
            }
            if (left >= from && right <= to) {
                updateFull(root, left, right, from, to, delta);
                return;
            }
            int middle = (left + right) >> 1;
            updatePreProcess(root, left, right, from, to, delta, middle);
            update(2 * root + 1, left, middle, from, to, delta);
            update(2 * root + 2, middle + 1, right, from, to, delta);
            updatePostProcess(root, left, right, from, to, delta, middle);
        }

        public long query(int from, int to) {
            return query(0, 0, size - 1, from, to);
        }

        protected long query(int root, int left, int right, int from, int to) {
            if (left > to || right < from) {
                return emptySegmentResult();
            }
            if (left >= from && right <= to) {
                return queryFull(root, left, right, from, to);
            }
            int middle = (left + right) >> 1;
            queryPreProcess(root, left, right, from, to, middle);
            long leftResult = query(2 * root + 1, left, middle, from, to);
            long rightResult = query(2 * root + 2, middle + 1, right, from, to);
            return queryPostProcess(root, left, right, from, to, middle, leftResult, rightResult);
        }

    }

    static class ArrayUtils {
        public static int[] range(int from, int to) {
            return Range.range(from, to).toArray();
        }

        public static int[] createOrder(int size) {
            return range(0, size);
        }

        public static int[] sort(int[] array, IntComparator comparator) {
            return sort(array, 0, array.length, comparator);
        }

        public static int[] sort(int[] array, int from, int to, IntComparator comparator) {
            if (from == 0 && to == array.length) {
                new IntArray(array).sort(comparator);
            } else {
                new IntArray(array).subList(from, to).sort(comparator);
            }
            return array;
        }

        public static int[] order(final int[] array) {
            return sort(createOrder(array.length), (first, second) -> Integer.compare(array[first], array[second]));
        }

        public static int[] unique(int[] array) {
            return new IntArray(array).unique().toArray();
        }

        public static int[] compress(int[]... arrays) {
            int totalLength = 0;
            for (int[] array : arrays) {
                totalLength += array.length;
            }
            int[] all = new int[totalLength];
            int delta = 0;
            for (int[] array : arrays) {
                System.arraycopy(array, 0, all, delta, array.length);
                delta += array.length;
            }
            sort(all, IntComparator.DEFAULT);
            all = unique(all);
            for (int[] array : arrays) {
                for (int i = 0; i < array.length; i++) {
                    array[i] = Arrays.binarySearch(all, array[i]);
                }
            }
            return all;
        }

    }

    static interface IntComparator {
        IntComparator DEFAULT = Integer::compare;

        int compare(int first, int second);

    }

    static interface IntStream extends Iterable<Integer>, Comparable<IntStream> {
        IntIterator intIterator();

        default Iterator<Integer> iterator() {
            return new Iterator<Integer>() {
                private IntIterator it = intIterator();

                public boolean hasNext() {
                    return it.isValid();
                }

                public Integer next() {
                    int result = it.value();
                    it.advance();
                    return result;
                }
            };
        }

        default int compareTo(IntStream c) {
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                int i = it.value();
                int j = jt.value();
                if (i < j) {
                    return -1;
                } else if (i > j) {
                    return 1;
                }
                it.advance();
                jt.advance();
            }
            if (it.isValid()) {
                return 1;
            }
            if (jt.isValid()) {
                return -1;
            }
            return 0;
        }

    }
}