Problem: Pink Floyd are pulling a prank on Roger Waters. They know he doesn't like [walls](https://www.youtube.com/watch?v=YR5ApYxkU-U), he wants to be able to walk freely, so they are blocking him from exiting his room which can be seen as a grid.

Roger Waters has a square grid of size n× n and he wants to traverse his grid from the upper left (1,1) corner to the lower right corner (n,n). Waters can move from a square to any other square adjacent by a side, as long as he is still in the grid. Also except for the cells (1,1) and (n,n) every cell has a value 0 or 1 in it.

Before starting his traversal he will pick either a 0 or a 1 and will be able to only go to cells values in which are equal to the digit he chose. The starting and finishing cells (1,1) and (n,n) are exempt from this rule, he may go through them regardless of picked digit. Because of this the cell (1,1) takes value the letter 'S' and the cell (n,n) takes value the letter 'F'.

For example, in the first example test case, he can go from (1, 1) to (n, n) by using the zeroes on this path: (1, 1), (2, 1), (2, 2), (2, 3), (3, 3), (3, 4), (4, 4)

The rest of the band (Pink Floyd) wants Waters to not be able to do his traversal, so while he is not looking they will invert at most two cells in the grid (from 0 to 1 or vice versa). They are afraid they will not be quick enough and asked for your help in choosing the cells.  Note that you cannot invert cells (1, 1) and (n, n).

We can show that there always exists a solution for the given constraints.

Also note that Waters will pick his digit of the traversal after the band has changed his grid, so he must not be able to reach (n,n) no matter what digit he picks.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 50). Description of the test cases follows.

The first line of each test case contains one integers n (3 ≤ n ≤ 200).

The following n lines of each test case contain the binary grid, square (1, 1) being colored in 'S' and square (n, n) being colored in 'F'.

The sum of values of n doesn't exceed 200.

Output

For each test case output on the first line an integer c (0 ≤ c ≤ 2) — the number of inverted cells.

In i-th of the following c lines, print the coordinates of the i-th cell you inverted. You may not invert the same cell twice.  Note that you cannot invert cells (1, 1) and (n, n).

Example

Input


3
4
S010
0001
1000
111F
3
S10
101
01F
5
S0101
00000
01111
11111
0001F


Output


1
3 4
2
1 2
2 1
0

Note

For the first test case, after inverting the cell, we get the following grid:
    
    
      
    S010  
    0001  
    1001  
    111F  
    

Solution (in JAVA):

Solution:
//package start;

import java.io.*;
import java.lang.*;
import java.util.*;
import java.util.function.BiFunction;

public class Main extends IO {

    public static void main(String[] args) throws Exception {
        int count = readInt();
        for (int i = 0; i < count; i++){
            int size = readInt();
            String[][] base = new String[size][];
            for (int j = 0; j < size; j++){
                base[j] = readArrayString("");
            }
            int answer = 0;
            StringBuilder strAnswer = new StringBuilder();
            for (int j = 0; j <= 1; j++){
                if (base[0][1].equals(j == 0 ? "1" : "0")){
                    answer++;
                    strAnswer.append("1 2");
                }
                if (base[1][0].equals(j == 0 ? "1" : "0")){
                    if (answer > 0){
                        strAnswer.append("\n");
                    }
                    answer++;
                    strAnswer.append("2 1");
                }
                if (base[size - 2][size - 1].equals(j== 0 ? "0" : "1")){
                    if (answer > 0){
                        strAnswer.append("\n");
                    }
                    answer++;
                    strAnswer.append(size - 1).append(" ").append(size);
                }
                if (base[size - 1][size - 2].equals(j== 0 ? "0" : "1")){
                    if (answer > 0){
                        strAnswer.append("\n");
                    }
                    answer++;
                    strAnswer.append(size).append(" ").append(size - 1);
                }
                if (answer <= 2){
                    break;
                }
                answer = 0;
                strAnswer.delete(0, strAnswer.length());
            }
            writeInt(answer, "\n");
            writeString(strAnswer.toString(), "\n");
        }
        print();
    }
}

class math {

    protected static long remains = 0x3B9ACA07; // 1000000007

    protected static int gcd(int a, int b) { // NOD
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    protected static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    protected static float gcd(float a, float b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    protected static double gcd(double a, double b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    protected static double lcm(double a, double b) { // NOK
        return a / gcd(a, b) * b;
    }

    protected static float lcm(float a, float b) { // NOK
        return a / gcd(a, b) * b;
    }

    protected static int lcm(int a, int b) { // NOK
        return a / gcd(a, b) * b;
    }

    protected static long lcm(long a, long b) {
        return a / gcd(a, b) * b;

    }

    protected static long mult(long a, long b){
        return ((a % remains) * (b % remains)) % remains;
    }

    protected static long binpow(long base, long power) {
        long res = 1;
        while (power != 0)
            if ((power & 1) == 1) {
                res = mult(res, base);
                power--;
            }
            else {
                base = mult(base, base);
                power >>= 1;
            }
        return res;
    }

    protected static double log(double value, int base) {
        return Math.log(value) / Math.log(base);
    }

    protected static long factorial(int number) {
        if (number < 0) {
            return 0;
        }
        return solveFactorial(number);
    }

    private static long solveFactorial(int number) {
        if (number > 0) {
            return solveFactorial(number - 1) * number;
        }
        return 1;
    }

}

class Int implements Comparable<Integer> {

    protected int value;

    Int(int value) {
        this.value = value;
    }

    public Int add(int value) {
        this.value += value;
        return this;
    }

    @Override
    public int compareTo(Integer o) {
        return (this.value < o) ? -1 : ((this.value == o) ? 0 : 1);
    }

    @Override
    public boolean equals(Object obj) {
        if (obj instanceof Integer) {
            return value == (Integer) obj;
        }
        return false;
    }

    @Override
    public int hashCode() {
        return value;
    }

    @Override
    protected void finalize() throws Throwable {
        super.finalize();
    }
}


class Fraction<T extends Number> extends Pair {

    private Fraction(T dividend, T divider) {
        super(dividend, divider);
        reduce();
    }

    protected static <T extends Number> Fraction<T> createFraction(T dividend, T divider) {
        return new Fraction<>(dividend, divider);
    }

    protected void reduce() {
        if (getFirstElement() instanceof Integer) {
            Integer Dividend = (Integer) getFirstElement();
            Integer Divider = (Integer) getSecondElement();
            int gcd = math.gcd(Dividend, Divider);
            setFirst(Dividend / gcd);
            setSecond(Divider / gcd);
        } else if (getFirstElement() instanceof Long) {
            Long Dividend = (Long) getFirstElement();
            Long Divider = (Long) getSecondElement();
            long gcd = math.gcd(Dividend, Divider);
            setFirst(Dividend / gcd);
            setSecond(Divider / gcd);
        } else if (getFirstElement() instanceof Float) {
            Float Dividend = (Float) getFirstElement();
            Float Divider = (Float) getSecondElement();
            float gcd = math.gcd(Dividend, Divider);
            setFirst(Dividend / gcd);
            setSecond(Divider / gcd);
        } else if (getFirstElement() instanceof Double) {
            Double Dividend = (Double) getFirstElement();
            Double Divider = (Double) getSecondElement();
            double gcd = math.gcd(Dividend, Divider);
            setFirst(Dividend / gcd);
            setSecond(Divider / gcd);
        }
    }

    protected void addWithoutReturn(Fraction number) throws UnsupportedOperationException {
        add(number, 0);
    }

    private Fraction add(Fraction number, int function) throws UnsupportedOperationException {
        if (getFirstElement() instanceof Integer && number.getFirstElement() instanceof Integer) {
            Integer Dividend = (Integer) getFirstElement();
            Integer Divider = (Integer) getSecondElement();
            Integer Dividend1 = (Integer) number.getFirstElement();
            Integer Divider1 = (Integer) number.getSecondElement();
            Integer lcm = math.lcm(Divider, Divider1);
            if (function == 0) {
                setFirst((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1);
                setSecond(lcm);
                reduce();
                return null;
            }
            Fraction result = Fraction.createFraction((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1, lcm);
            result.reduce();
            return result;

        } else if (getFirstElement() instanceof Long && number.getFirstElement() instanceof Long) {
            Long Dividend = (Long) getFirstElement();
            Long Divider = (Long) getSecondElement();
            Long Dividend1 = (Long) number.getFirstElement();
            Long Divider1 = (Long) number.getSecondElement();
            Long lcm = math.lcm(Divider, Divider1);
            if (function == 0) {
                setFirst((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1);
                setSecond(lcm);
                reduce();
                return null;
            }
            Fraction result = Fraction.createFraction((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1, lcm);
            result.reduce();
            return result;
        } else if (getFirstElement() instanceof Float && number.getFirstElement() instanceof Float) {
            Float Dividend = (Float) getFirstElement();
            Float Divider = (Float) getSecondElement();
            Float Dividend1 = (Float) number.getFirstElement();
            Float Divider1 = (Float) number.getSecondElement();
            Float lcm = math.lcm(Divider, Divider1);
            if (function == 0) {
                setFirst((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1);
                setSecond(lcm);
                reduce();
                return null;
            }
            Fraction result = Fraction.createFraction((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1, lcm);
            result.reduce();
            return result;
        } else if (getFirstElement() instanceof Double && number.getFirstElement() instanceof Double) {
            Double Dividend = (Double) getFirstElement();
            Double Divider = (Double) getSecondElement();
            Double Dividend1 = (Double) number.getFirstElement();
            Double Divider1 = (Double) number.getSecondElement();
            Double lcm = math.lcm(Divider, Divider1);
            if (function == 0) {
                setFirst((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1);
                setSecond(lcm);
                reduce();
                return null;
            }
            Fraction result = Fraction.createFraction((lcm / Divider) * Dividend + (lcm / Divider1) * Dividend1, lcm);
            result.reduce();
            return result;
        } else {
            throw new UnsupportedOperationException();
        }
    }

    protected Fraction addWithReturn(Fraction number) {
        return add(number, 1);
    }

    protected void multiplyWithoutReturn(Fraction number) throws UnsupportedOperationException {
        multiply(number, 0);
    }

    protected Fraction multiplyWithReturn(Fraction number) throws UnsupportedOperationException {
        return multiply(number, 1);
    }

    private Fraction multiply(Fraction number, int function) throws UnsupportedOperationException {
        if (getFirstElement() instanceof Integer && number.getFirstElement() instanceof Integer) {
            Integer first = (Integer) getFirstElement() * (Integer) number.getFirstElement();
            Integer second = (Integer) getSecondElement() * (Integer) number.getSecondElement();
            if (function == 0) {
                setFirst(first);
                setSecond(second);
                reduce();
                return null;
            }
            Fraction answer = Fraction.createFraction(first, second);
            answer.reduce();
            return answer;
        } else if (getFirstElement() instanceof Long && number.getFirstElement() instanceof Long) {
            Long first = (Long) getFirstElement() * (Long) number.getFirstElement();
            Long second = (Long) getSecondElement() * (Long) number.getSecondElement();
            if (function == 0) {
                setFirst(first);
                setSecond(second);
                reduce();
                return null;
            }
            Fraction answer = Fraction.createFraction(first, second);
            answer.reduce();
            return answer;

        } else if (getFirstElement() instanceof Float && number.getFirstElement() instanceof Float) {
            Float first = (Float) getFirstElement() * (Float) number.getFirstElement();
            Float second = (Float) getSecondElement() * (Float) number.getSecondElement();
            if (function == 0) {
                setFirst(first);
                setSecond(second);
                reduce();
                return null;
            }
            Fraction answer = Fraction.createFraction(first, second);
            answer.reduce();
            return answer;
        } else if (getFirstElement() instanceof Double && number.getFirstElement() instanceof Double) {
            Double first = (Double) getFirstElement() * (Double) number.getFirstElement();
            Double second = (Double) getSecondElement() * (Double) number.getSecondElement();
            if (function == 0) {
                setFirst(first);
                setSecond(second);
                reduce();
                return null;
            }
            Fraction answer = Fraction.createFraction(first, second);
            answer.reduce();
            return answer;
        } else {
            throw new UnsupportedOperationException();
        }
    }
}

class Pair<T, T1> implements Cloneable {

    private T first;
    private T1 second;

    Pair(T obj, T1 obj1) {
        first = obj;
        second = obj1;
    }

    protected static <T, T1> Pair<T, T1> createPair(T element, T1 element1) {
        return new Pair<>(element, element1);
    }

    protected T getFirstElement() {
        return first;
    }

    protected T1 getSecondElement() {
        return second;
    }

    protected void setFirst(T element) {
        first = element;
    }

    protected void setSecond(T1 element) {
        second = element;
    }

    @Override
    public boolean equals(Object obj) {
        if (!(obj instanceof Pair)) {
            return false;
        }
        Pair pair = (Pair) obj;
        return first.equals(pair.first) && second.equals(pair.second);
    }

    @Override
    public int hashCode() {
        int hashCode = 1;
        hashCode = 31 * hashCode + (first == null ? 0 : first.hashCode());
        return 31 * hashCode + (second == null ? 0 : second.hashCode());
    }

    @Override
    public Object clone() {
        return Pair.createPair(first, second);
    }
}

class Graph {

    private int[][] base;
    private boolean[] used;
    private int quantity;
    private Integer[] ancestor;

    public int[][] getBase() {
        return base;
    }

    public boolean[] getUsed() {
        return used;
    }

    public int getQuantity() {
        return quantity;
    }

    public Integer[] getAncestor() {
        return ancestor;
    }

    public void setBase(int[][] base) {
        this.base = base;
    }

    protected void start(int length) {
        used = new boolean[length];
        ancestor = new Integer[length];
        Arrays.fill(ancestor, -1);
        quantity = 0;
    }


    protected void edgesMatrixToDefault(int length, int inputQuantity, boolean readConsole, int[][] value) throws Exception {
        base = new int[length][];
        List<ArrayList<Integer>> inputBase = new ArrayList<>();
        for (int i = 0; i < length; i++) {
            inputBase.add(new ArrayList<>());
        }
        for (int i = 0; i < inputQuantity; i++) {
            int[] input = readConsole ? IO.readArrayInt(" ") : value[i];
            inputBase.get(input[0] - 1).add(input[1] - 1);
            inputBase.get(input[0] - 1).add(input[2]); // price
            inputBase.get(input[1] - 1).add(input[0] - 1);
            inputBase.get(input[1] - 1).add(input[2]); // price
        }
        for (int i = 0; i < length; i++) {
            base[i] = inputBase.get(i).stream().mapToInt(Integer::intValue).toArray();
        }
        start(length);
    }

    protected void adjacencyMatrixToDefault(int length, int not, boolean readConsole, int[][] value) throws Exception {
        this.base = new int[length][];
        List<Integer> buffer = new ArrayList<>();
        for (int i = 0; i < length; i++) {
            int[] InputArray = readConsole ? IO.readArrayInt(" ") : value[i];
            for (int index = 0; index < length; index++) {
                if (i != index && InputArray[index] != not) {
                    buffer.add(index);
                    // buffer.add(InputArray[index]); // price
                }
            }
            this.base[i] = buffer.stream().mapToInt(Integer::intValue).toArray();
            buffer.clear();
        }
        start(length);
    }

    protected int dfs(int position) throws Exception {
        used[position] = true;
        int next;
        int count = 0;
        for (int index = 0; index < base[position].length; index += 2) {
            next = base[position][index];
            if (!used[next]) {
                ancestor[next] = position;
                count += dfs(next);
            }
             /*else {
                if (next != ancestor[position]) { // if cycle
                    throw new Exception();
                }
            }*/
        }
        if (base[position].length == 2 && base[position][0] == ancestor[position]) {
            return 1;
        }
        return count;
    }

    protected int dijkstra(int start, int stop, int size) {
        start--;
        stop--;
        int[] dist = new int[size];
        for (int i = 0; i < size; i++) {
            if (i != start) {
                dist[i] = Integer.MAX_VALUE;
            }
            ancestor[i] = start;
        }

        Queue<int[]> queue = new PriorityQueue<>(Comparator.comparingInt((int[] ints) -> ints[1]));
        queue.add(new int[]{start, 0});
        int position;
        int[] getQueue;
        while (queue.size() != 0) {
            getQueue = queue.poll();
            position = getQueue[0];
            if (getQueue[1] > dist[position]) {
                continue;
            }
            for (int index = 0; index < this.base[position].length; index += 2) {
                if (dist[position] + this.base[position][index + 1] < dist[this.base[position][index]] && !this.used[this.base[position][index]]) {
                    dist[this.base[position][index]] = dist[position] + this.base[position][index + 1];
                    this.ancestor[this.base[position][index]] = position;
                    queue.add(new int[]{this.base[position][index], dist[this.base[position][index]]});
                }
            }
            used[position] = true;
        }
        return dist[stop] == Integer.MAX_VALUE ? -1 : dist[stop];
    }

    protected static boolean solveFloydWarshall(int[][] base, int length, int not) {
        for (int k = 0; k < length; k++) {
            for (int i = 0; i < length; i++) {
                for (int j = 0; j < length; j++) {
                    if (base[i][k] == not || base[k][j] == not) {
                        continue;
                    }
                    int total = base[i][k] + base[k][j];
                    if (base[i][j] != not) {
                        base[i][j] = Math.min(base[i][j], total);
                    } else {
                        base[i][j] = total;
                    }
                }
            }
        }
        for (int index = 0; index < length; index++) {
            if (base[index][index] != 0) { // if cycle
                return false;
            }
        }
        return true;
    }

    protected static Pair<Long, int[][]> solveKruskal(int[][] edgesMatrix, final int countVertex, final int indexSort) {
        int[][] answer = new int[countVertex - 1][2];
        long sum = 0;
        Arrays.sort(edgesMatrix, Comparator.comparingInt(value -> value[indexSort]));
        SystemOfDisjointSets dsu = new SystemOfDisjointSets(countVertex);
        for (int i = 0; i < countVertex; i++) {
            dsu.makeSet(i);
        }
        int index = 0;
        for (int[] value : edgesMatrix) {
            if (dsu.mergeSets(value[0], value[1])) {
                sum += value[indexSort];
                answer[index] = new int[]{value[0], value[1]};
                index++;
            }
        }
        if (index < countVertex - 1) {
            return Pair.createPair(null, null);
        }
        return Pair.createPair(sum, answer);
    }

    static class SegmentTree {

        private int[] segmentArray;
        private BiFunction<Integer, Integer, Integer> function;

        protected void setSegmentArray(int[] segmentArray) {
            this.segmentArray = segmentArray;
        }

        protected int[] getSegmentArray() {
            return segmentArray.clone();
        }

        protected void setFunction(BiFunction<Integer, Integer, Integer> function) {
            this.function = function;
        }

        protected BiFunction<Integer, Integer, Integer> getFunction() {
            return function;
        }

        SegmentTree() {

        }

        SegmentTree(int[] startBase, int neutral, BiFunction<Integer, Integer, Integer> function) {
            this.function = function;
            int length = startBase.length;
            int[] base;
            if ((length & (length - 1)) != 0) {
                int pow = 0;
                while (length > 0) {
                    length >>= 1;
                    pow++;
                }
                pow--;
                base = new int[2 << pow];
                System.arraycopy(startBase, 0, base, 0, startBase.length);
                Arrays.fill(base, startBase.length, base.length, neutral);

            } else {
                base = startBase;
            }
            segmentArray = new int[base.length << 1]; // maybe * 4
            Arrays.fill(segmentArray, neutral);
            inDepth(base, 1, 0, base.length - 1);
        }

        private void inDepth(int[] base, int position, int low, int high) {
            if (low == high) {
                segmentArray[position] = base[low];
            } else {
                int mid = (low + high) >> 1;
                inDepth(base, position << 1, low, mid);
                inDepth(base, (position << 1) + 1, mid + 1, high);
                segmentArray[position] = function.apply(segmentArray[position << 1], segmentArray[(position << 1) + 1]);
            }
        }

        protected int getValue(int left, int right, int neutral) {
            return findValue(1, 0, ((segmentArray.length) >> 1) - 1, left, right, neutral);
        }

        private int findValue(int position, int low, int high, int left, int right, int neutral) {
            if (left > right) {
                return neutral;
            }
            if (left == low && right == high) {
                return segmentArray[position];
            }
            int mid = (low + high) >> 1;
            return function.apply(findValue(position << 1, low, mid, left, Math.min(right, mid), neutral),
                    findValue((position << 1) + 1, mid + 1, high, Math.max(left, mid + 1), right, neutral));
        }

        protected void replaceValue(int index, int value) {
            update(1, 0, (segmentArray.length >> 1) - 1, index, value);
        }

        private void update(int position, int low, int high, int index, int value) {
            if (low == high) {
                segmentArray[position] = value;
            } else {
                int mid = (low + high) >> 1;
                if (index <= mid) {
                    update(position << 1, low, mid, index, value);
                } else {
                    update((position << 1) + 1, mid + 1, high, index, value);
                }
                segmentArray[position] = function.apply(segmentArray[position << 1], segmentArray[(position << 1) + 1]);
            }
        }
    }

    static class SegmentTreeGeneric<T> {

        private Object[] segmentArray;
        private BiFunction<T, T, T> function;

        protected void setSegmentArray(T[] segmentArray) {
            this.segmentArray = segmentArray;
        }

        protected Object getSegmentArray() {
            return segmentArray.clone();
        }

        protected void setFunction(BiFunction<T, T, T> function) {
            this.function = function;
        }

        protected BiFunction<T, T, T> getFunction() {
            return function;
        }

        SegmentTreeGeneric() {

        }

        SegmentTreeGeneric(T[] startBase, T neutral, BiFunction<T, T, T> function) {
            this.function = function;
            int length = startBase.length;
            Object[] base;
            if ((length & (length - 1)) != 0) {
                int pow = 0;
                while (length > 0) {
                    length >>= 1;
                    pow++;
                }
                pow--;
                base = new Object[2 << pow];
                System.arraycopy(startBase, 0, base, 0, startBase.length);
                Arrays.fill(base, startBase.length, base.length, neutral);

            } else {
                base = startBase;
            }
            segmentArray = new Object[base.length << 1]; // maybe * 4
            Arrays.fill(segmentArray, neutral);
            inDepth(base, 1, 0, base.length - 1);
        }

        private void inDepth(Object[] base, int position, int low, int high) {
            if (low == high) {
                segmentArray[position] = base[low];
            } else {
                int mid = (low + high) >> 1;
                inDepth(base, position << 1, low, mid);
                inDepth(base, (position << 1) + 1, mid + 1, high);
                segmentArray[position] = function.apply((T) segmentArray[position << 1], (T) segmentArray[(position << 1) + 1]);
            }
        }

        protected T getValue(int left, int right, T neutral) {
            return findValue(1, 0, ((segmentArray.length) >> 1) - 1, left, right, neutral);
        }

        private T findValue(int position, int low, int high, int left, int right, T neutral) {
            if (left > right) {
                return neutral;
            }
            if (left == low && right == high) {
                return (T) segmentArray[position];
            }
            int mid = (low + high) >> 1;
            return function.apply(findValue(position << 1, low, mid, left, Math.min(right, mid), neutral),
                    findValue((position << 1) + 1, mid + 1, high, Math.max(left, mid + 1), right, neutral));
        }

        protected void replaceValue(int index, T value) {
            update(1, 0, (segmentArray.length >> 1) - 1, index, value);
        }

        private void update(int position, int low, int high, int index, T value) {
            if (low == high) {
                segmentArray[position] = value;
            } else {
                int mid = (low + high) >> 1;
                if (index <= mid) {
                    update(position << 1, low, mid, index, value);
                } else {
                    update((position << 1) + 1, mid + 1, high, index, value);
                }
                segmentArray[position] = function.apply((T) segmentArray[position << 1], (T) segmentArray[(position << 1) + 1]);
            }
        }
    }
}

class SystemOfDisjointSets {

    private int[] rank;
    private int[] dsu;

    SystemOfDisjointSets(int size) {
        this.rank = new int[size];
        this.dsu = new int[size];
    }

    protected void makeSet(int value) {
        dsu[value] = value;
        rank[value] = 0;
    }

    protected int findSet(int value) {
        if (value == dsu[value]) {
            return value;
        }
        return dsu[value] = findSet(dsu[value]);
    }

    protected boolean mergeSets(int first, int second) {
        first = findSet(first);
        second = findSet(second);
        if (first != second) {
            if (rank[first] < rank[second]) {
                int number = first;
                first = second;
                second = number;
            }
            dsu[second] = first;
            if (rank[first] == rank[second]) {
                rank[first]++;
            }
            return true;
        }
        return false;
    }
}

interface Array {
    void useArray(int[] a);
}

interface Method {
    void use();
}

class FastSort {

    protected static int[] sort(int[] array, int ShellHeapMergeMyInsertionSort) {
        sort(array, ShellHeapMergeMyInsertionSort, array.length);
        return array;
    }

    protected static int[] sortClone(int[] array, int ShellHeapMergeMyInsertionSort) {
        int[] base = array.clone();
        sort(base, ShellHeapMergeMyInsertionSort, array.length);
        return base;
    }

    private static void sort(int[] array, int ShellHeapMergeMyInsertionSort, int length) {
        if (ShellHeapMergeMyInsertionSort < 0 || ShellHeapMergeMyInsertionSort > 4) {
            Random random = new Random();
            ShellHeapMergeMyInsertionSort = random.nextInt(4);
        }
        if (ShellHeapMergeMyInsertionSort == 0) {
            ShellSort(array);
        } else if (ShellHeapMergeMyInsertionSort == 1) {
            HeapSort(array);
        } else if (ShellHeapMergeMyInsertionSort == 2) {
            MergeSort(array, 0, length - 1);
        } else if (ShellHeapMergeMyInsertionSort == 3) {
            straightMergeSort(array, length);
        } else if (ShellHeapMergeMyInsertionSort == 4) {
            insertionSort(array);
        }
    }

    private static void straightMergeSort(int[] array, int size) {
        if (size == 0) {
            return;
        }
        int length = (size >> 1) + ((size % 2) == 0 ? 0 : 1);
        Integer[][] ZeroBuffer = new Integer[length + length % 2][2];
        Integer[][] FirstBuffer = new Integer[0][0];
        for (int index = 0; index < length; index++) {
            int ArrayIndex = index << 1;
            int NextArrayIndex = (index << 1) + 1;
            if (NextArrayIndex < size) {
                if (array[ArrayIndex] > array[NextArrayIndex]) {
                    ZeroBuffer[index][0] = array[NextArrayIndex];
                    ZeroBuffer[index][1] = array[ArrayIndex];
                } else {
                    ZeroBuffer[index][0] = array[ArrayIndex];
                    ZeroBuffer[index][1] = array[NextArrayIndex];
                }
            } else {
                ZeroBuffer[index][0] = array[ArrayIndex];
            }
        }
        boolean position = false;
        int pointer0, pointer, pointer1, number = 4, NewPointer, count;
        Integer[][] NewBuffer;
        Integer[][] OldBuffer;
        length = (size >> 2) + ((size % 4) == 0 ? 0 : 1);
        while (true) {
            pointer0 = 0;
            count = (number >> 1) - 1;
            if (!position) {
                FirstBuffer = new Integer[length + length % 2][number];
                NewBuffer = FirstBuffer;
                OldBuffer = ZeroBuffer;
            } else {
                ZeroBuffer = new Integer[length + length % 2][number];
                NewBuffer = ZeroBuffer;
                OldBuffer = FirstBuffer;
            }
            for (int i = 0; i < length; i++) {
                pointer = 0;
                pointer1 = 0;
                NewPointer = pointer0 + 1;
                if (length == 1) {
                    for (int g = 0; g < size; g++) {
                        if (pointer > count || OldBuffer[pointer0][pointer] == null) {
                            array[g] = OldBuffer[NewPointer][pointer1];
                            pointer1++;
                        } else if (pointer1 > count || OldBuffer[NewPointer][pointer1] == null) {
                            if (OldBuffer[pointer0][pointer] == null) {
                                continue;
                            }
                            array[g] = OldBuffer[pointer0][pointer];
                            pointer++;
                        } else if (OldBuffer[pointer0][pointer] >= OldBuffer[NewPointer][pointer1]) {
                            array[g] = OldBuffer[NewPointer][pointer1];
                            pointer1++;
                        } else {
                            array[g] = OldBuffer[pointer0][pointer];
                            pointer++;
                        }
                    }
                    return;
                }
                for (int g = 0; g < number; g++) {
                    if (pointer > count || OldBuffer[pointer0][pointer] == null) {
                        if (OldBuffer[NewPointer][pointer1] == null) {
                            continue;
                        }
                        NewBuffer[i][g] = OldBuffer[NewPointer][pointer1];
                        pointer1++;
                    } else if (pointer1 > count || OldBuffer[NewPointer][pointer1] == null) {
                        if (OldBuffer[pointer0][pointer] == null) {
                            continue;
                        }
                        NewBuffer[i][g] = OldBuffer[pointer0][pointer];
                        pointer++;
                    } else if (OldBuffer[pointer0][pointer] >= OldBuffer[NewPointer][pointer1]) {
                        NewBuffer[i][g] = OldBuffer[NewPointer][pointer1];
                        pointer1++;
                    } else {
                        NewBuffer[i][g] = OldBuffer[pointer0][pointer];
                        pointer++;
                    }
                }
                pointer0 += 2;
            }
            position = !position;
            length = (length >> 1) + length % 2;
            number <<= 1;
        }
    }

    private static void ShellSort(int[] array) {
        int j;
        for (int gap = (array.length >> 1); gap > 0; gap >>= 1) {
            for (int i = gap; i < array.length; i++) {
                int temp = array[i];
                for (j = i; j >= gap && array[j - gap] > temp; j -= gap) {
                    array[j] = array[j - gap];
                }
                array[j] = temp;
            }
        }
    }

    private static void HeapSort(int[] array) {
        for (int i = (array.length >> 1) - 1; i >= 0; i--)
            shiftDown(array, i, array.length);
        for (int i = array.length - 1; i > 0; i--) {
            swap(array, 0, i);
            shiftDown(array, 0, i);
        }
    }

    private static void shiftDown(int[] array, int i, int n) {
        int child;
        int tmp;
        for (tmp = array[i]; leftChild(i) < n; i = child) {
            child = leftChild(i);
            if (child != n - 1 && (array[child] < array[child + 1]))
                child++;
            if (tmp < array[child])
                array[i] = array[child];
            else
                break;
        }
        array[i] = tmp;
    }

    private static int leftChild(int i) {
        return (i << 1) + 1;
    }

    private static void swap(int[] array, int i, int j) {
        int temp = array[i];
        array[i] = array[j];
        array[j] = temp;
    }

    private static void MergeSort(int[] array, int low, int high) {
        if (low < high) {
            int mid = (low + high) >> 1;
            MergeSort(array, low, mid);
            MergeSort(array, mid + 1, high);
            merge(array, low, mid, high);
        }
    }

    private static void merge(int[] array, int low, int mid, int high) {
        int n = high - low + 1;
        int[] Temp = new int[n];
        int i = low, j = mid + 1;
        int k = 0;
        while (i <= mid || j <= high) {
            if (i > mid)
                Temp[k++] = array[j++];
            else if (j > high)
                Temp[k++] = array[i++];
            else if (array[i] < array[j])
                Temp[k++] = array[i++];
            else
                Temp[k++] = array[j++];
        }
        for (j = 0; j < n; j++)
            array[low + j] = Temp[j];
    }

    private static void insertionSort(int[] elements) {
        for (int i = 1; i < elements.length; i++) {
            int key = elements[i];
            int j = i - 1;
            while (j >= 0 && key < elements[j]) {
                elements[j + 1] = elements[j];
                j--;
            }
            elements[j + 1] = key;
        }
    }
}

class IO {

    private static BufferedReader read;
    private static boolean fileInput = false;
    private static BufferedWriter write;
    private static boolean fileOutput = false;

    public static void setFileInput(boolean fileInput) {
        IO.fileInput = fileInput;
    }

    public static void setFileOutput(boolean fileOutput) {
        IO.fileOutput = fileOutput;
    }

    private static void startInput() {
        try {
            read = new BufferedReader(fileInput ? new FileReader("input.txt") : new InputStreamReader(System.in));
        } catch (Exception error) {
        }
    }

    private static void startOutput() {
        try {
            write = new BufferedWriter(fileOutput ? new FileWriter("output.txt") : new OutputStreamWriter(System.out));
        } catch (Exception error) {
        }
    }

    protected static int readInt() throws Exception {
        if (read == null) {
            startInput();
        }
        return Integer.parseInt(read.readLine());
    }

    protected static long readLong() throws Exception {
        if (read == null) {
            startInput();
        }
        return Long.parseLong(read.readLine());
    }

    protected static String readString() throws Exception {
        if (read == null) {
            startInput();
        }
        return read.readLine();
    }

    protected static int[] readArrayInt(String split) throws Exception {
        if (read == null) {
            startInput();
        }
        return Arrays.stream(read.readLine().split(split)).mapToInt(Integer::parseInt).toArray();
    }

    protected static long[] readArrayLong(String split) throws Exception {
        if (read == null) {
            startInput();
        }
        return Arrays.stream(read.readLine().split(split)).mapToLong(Long::parseLong).toArray();
    }

    protected static String[] readArrayString(String split) throws Exception {
        if (read == null) {
            startInput();
        }
        return read.readLine().split(split);
    }

    protected static void writeArray(int[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(Integer.toString(array[index]));
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception error) {
        }
    }

    protected static void writeArray(Integer[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(Integer.toString(array[index]));
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception error) {
        }
    }

    protected static void writeArray(long[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(Long.toString(array[index]));
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception error) {
        }
    }

    protected static void writeArray(Long[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(Long.toString(array[index]));
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception error) {
        }
    }

    public static void writeArray(String[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(array[index]);
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception ignored) {
        }
    }

    protected static void writeArray(boolean[] array, String split, boolean enter) {
        if (write == null) {
            startOutput();
        }
        try {
            int length = array.length;
            for (int index = 0; index < length; index++) {
                write.write(Boolean.toString(array[index]));
                if (index + 1 != length) {
                    write.write(split);
                }
            }
            if (enter) {
                writeEnter();
            }
        } catch (Exception ignored) {
        }
    }

    protected static void writeInt(int number, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(Integer.toString(number));
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeInt(Integer number, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(Integer.toString(number));
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeLong(long number, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(Long.toString(number));
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeLong(Long number, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(Long.toString(number));
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeString(String word, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(word);
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeBoolean(boolean value, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(value ? "true" : "false");
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeBoolean(Boolean value, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(value ? "true" : "false");
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeChar(char word, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(word);
            write.write(end);
        } catch (Exception ignored) {
        }
    }

    protected static void writeChar(Character word, String end) {
        if (write == null) {
            startOutput();
        }
        try {
            write.write(word);
            write.write(end);
        } catch (Exception ignored) {
        }
    }


    protected static void writeEnter() {
        if (write == null) {
            startOutput();
        }
        try {
            write.newLine();
        } catch (Exception ignored) {
        }
    }

    protected static void print(boolean exit) throws Exception {
        if (exit) {
            print();
        } else {
            write.flush();
        }
    }

    protected static void print() throws Exception {
        if (write == null) {
            return;
        }
        write.flush();
        if (read != null) {
            read.close();
        }
        write.close();
    }
}