Problem:
Score : 400 points

Problem Statement

There is a grid of square cells with H horizontal rows and W vertical columns. The cell at the i-th row and the j-th column will be denoted as Cell (i, j).

In Cell (i, j), a_{ij} coins are placed.

You can perform the following operation any number of times:

Operation: Choose a cell that was not chosen before and contains one or more coins, then move one of those coins to a vertically or horizontally adjacent cell.

Maximize the number of cells containing an even number of coins.

Constraints

All values in input are integers.

1 \leq H, W \leq 500

0 \leq a_{ij} \leq 9

Input

Input is given from Standard Input in the following format:

H W
a_{11} a_{12} ... a_{1W}
a_{21} a_{22} ... a_{2W}
:
a_{H1} a_{H2} ... a_{HW}

Output

Print a sequence of operations that maximizes the number of cells containing an even number of coins, in the following format:

N
y_1 x_1 y_1' x_1'
y_2 x_2 y_2' x_2'
:
y_N x_N y_N' x_N'

That is, in the first line, print an integer N between 0 and H \times W (inclusive), representing the number of operations.

In the (i+1)-th line (1 \leq i \leq N), print four integers y_i, x_i, y_i' and x_i' (1 \leq y_i, y_i' \leq H and 1 \leq x_i, x_i' \leq W), representing the i-th operation. These four integers represents the operation of moving one of the coins placed in Cell (y_i, x_i) to a vertically or horizontally adjacent cell, (y_i', x_i').

Note that if the specified operation violates the specification in the problem statement or the output format is invalid, it will result in Wrong Answer.

Sample Input 1

2 3
1 2 3
0 1 1

Sample Output 1

3
2 2 2 3
1 1 1 2
1 3 1 2

Every cell contains an even number of coins after the following sequence of operations:

Move the coin in Cell (2, 2) to Cell (2, 3).

Move the coin in Cell (1, 1) to Cell (1, 2).

Move one of the coins in Cell (1, 3) to Cell (1, 2).

Sample Input 2

3 2
1 0
2 1
1 0

Sample Output 2

3
1 1 1 2
1 2 2 2
3 1 3 2

Sample Input 3

1 5
9 9 9 9 9

Sample Output 3

2
1 1 1 2
1 3 1 4

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.io.*;

import static java.lang.Math.*;
import static java.lang.Math.min;

import java.math.BigDecimal;
import java.util.*;

/**
 * @author baito
 */
@SuppressWarnings("unchecked")
public class Main {
    static boolean DEBUG = true;
    static StringBuilder sb = new StringBuilder();
    static int INF = 1234567890;
    static int MINF = -1234567890;
    static long LINF = 123456789123456789L;
    static long MLINF = -123456789123456789L;
    static long MOD = 1000000007;
    static double EPS = 1e-10;
    static int[] y4 = {0, 1, 0, -1};
    static int[] x4 = {1, 0, -1, 0};
    static int[] y8 = {0, 1, 0, -1, -1, 1, 1, -1};
    static int[] x8 = {1, 0, -1, 0, 1, -1, 1, -1};
    static ArrayList<Long> Fa;
    static boolean[] isPrime;
    static ArrayList<Integer> primes;
    static char[][] ban;
    static long maxRes = MLINF;
    static long minRes = LINF;

    static int N;
    static int[][] A;
    static boolean[][] used;

    public static void solve() throws Exception {
        //longを忘れるなオーバーフローするぞ
        int H = ni();
        int W = ni();
        A = nit(H, W);
        used = new boolean[H + 1][W + 1];
        int fh = -1, fw = -1, th = -1, tw = -1;
        int sousa = 0;
        for (int hi = 0; hi < H; hi++) {
            for (int wi = 0; wi < W; wi++) {
                if (A[hi][wi] % 2 == 1 && !used[hi][wi]) {
                    if (fh != -1) {
                        th = hi;
                        tw = wi;
                        sousa += move(fh, fw, th, tw);
                        used[fh][fw] = true;
                        used[th][tw] = true;
                        fh = -1;
                        fw = -1;
                        th = -1;
                        tw = -1;

                    } else {
                        fh = hi;
                        fw = wi;
                    }
                }
            }
        }
        System.out.println(sousa);
        print(res);
    }

    static class Four implements Comparable<Four> {
        int h, w, nh, nw, dis;

        Four(int h, int w, int nh, int nw, int dis) {
            this.h = h;
            this.w = w;
            this.nh = nh;
            this.nw = nw;
            this.dis = dis;
        }

        @Override
        public int compareTo(Four f) {
            return this.dis - f.dis;
        }

    }

    static ArrayList<String> res = new ArrayList<>();

    public static int move(int h, int w, int nh, int nw) {
        boolean ok = true;
        for (int tw = w; ; ) {
            if (tw == nw) break;
            if (tw < nw) tw++;
            else tw--;
            if (h == nh && tw == nw) break;
            if (used[h][tw]) ok = false;
        }
        h++;
        w++;
        nh++;
        nw++;
        int cou = 0;
        if (ok) {
            for (int wi = w; ; ) {
                if (wi == nw) break;
                int tw = wi;
                if (wi < nw) tw++;
                else tw--;
                res.add(h + " " + wi + " " + h + " " + tw);
                wi = tw;
                cou++;
            }
            for (int hi = h; ; ) {
                if (hi == nh) break;
                int th = hi;
                if (hi < nh) th++;
                else th--;
                res.add(hi + " " + nw + " " + th + " " + nw);
                hi = th;
                cou++;
            }
        } else {
            for (int hi = h; ; ) {
                if (hi == nh) break;
                int th = hi;
                if (hi < nh) th++;
                else th--;
                res.add(hi + " " + w + " " + th + " " + w);
                hi = th;
                cou++;
            }
            for (int wi = w; ; ) {
                if (wi == nw) break;
                int tw = wi;
                if (wi < nw) tw++;
                else tw--;
                res.add(nh + " " + wi + " " + nh + " " + tw);
                wi = tw;
                cou++;
            }
        }
        return cou;
    }

    //値を渡す際は半開区間
    static class RectangleSum {
        //半開区間 0は0
        long[][] rui;
        int H, W;

        RectangleSum(long[][] ori) {
            H = ori.length;
            W = ori[0].length;
            rui = new long[H + 1][W + 1];
            for (int hi = 0; hi < H; hi++) {
                for (int wi = 0; wi < W; wi++) {
                    rui[hi + 1][wi + 1] = ori[hi][wi];
                }
            }
            for (int hi = 1; hi < H + 1; hi++) {
                for (int wi = 1; wi < W + 1; wi++) {
                    rui[hi][wi] += rui[hi - 1][wi];
                    rui[hi][wi] += rui[hi][wi - 1];
                    rui[hi][wi] -= rui[hi - 1][wi - 1];
                }
            }
        }

        RectangleSum(int[][] ori) {
            H = ori.length;
            W = ori[0].length;
            rui = new long[H + 1][W + 1];
            for (int hi = 0; hi < H; hi++) {
                for (int wi = 0; wi < W; wi++) {
                    rui[hi + 1][wi + 1] = ori[hi][wi];
                }
            }
            for (int hi = 1; hi < H + 1; hi++) {
                for (int wi = 1; wi < W + 1; wi++) {
                    rui[hi][wi] += rui[hi - 1][wi];
                    rui[hi][wi] += rui[hi][wi - 1];
                    rui[hi][wi] -= rui[hi - 1][wi - 1];
                }
            }
        }

        //半開区間
        public long getSum(int left, int right, int top, int bottom) {
            if (right > W || bottom > H) return 0;
            if (left < 0 || top < 0) return 0;
            if (top >= bottom || left >= right) return 0;
            long res = rui[bottom][right];
            res -= rui[top][right];
            res -= rui[bottom][left];
            res += rui[top][left];
            return res;
        }

    }

    public static boolean calc(long va) {
        //貪欲にギリギリセーフを選んでいく。
        int v = (int) va;
        return true;
    }

    //条件を満たす最大値、あるいは最小値を求める
    static int mgr(long ok, long ng) {
        //int ok = 0; //解が存在する
        //int ng = N; //解が存在しない
        while (Math.abs(ok - ng) > 1) {
            long mid;
            if (ok < 0 && ng > 0 || ok > 0 && ng < 0) mid = (ok + ng) / 2;
            else mid = ok + (ng - ok) / 2;

            if (calc(mid)) {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        if (calc(ok)) return (int) ok;
        else return -1;
    }

    static ArrayList<Integer> divisors(int n) {
        ArrayList<Integer> res = new ArrayList<>();
        for (int i = 1; i <= Math.sqrt(n); i++) {
            if (n % i == 0) {
                res.add(i);
                if (i != n / i) res.add(n / i);
            }
        }
        return res;
    }

    static ArrayList<Long> divisors(long n) {
        ArrayList<Long> res = new ArrayList<>();
        for (long i = 1; i <= Math.sqrt(n); i++) {
            if (n % i == 0) {
                res.add(i);
                if (i != n / i) res.add(n / i);
            }
        }
        return res;
    }

    static ArrayList<Integer> factorization(int n) {
        if (primes == null) setPrimes();
        ArrayList<Integer> fact = new ArrayList<>();
        for (int p : primes) {
            if (n % p == 0) fact.add(p);
            while (n % p == 0) n /= p;
            if (n == 1) break;
        }
        if (n != 1) fact.add(n);
        return fact;
    }

    boolean equal(double a, double b) {
        return a == 0 ? abs(b) < EPS : abs((a - b) / a) < EPS;
    }

    public static void matPrint(long[][] a) {
        for (int hi = 0; hi < a.length; hi++) {
            for (int wi = 0; wi < a[0].length; wi++) {
                System.out.print(a[hi][wi] + " ");
            }
            System.out.println("");
        }
    }

    //rにlを掛ける l * r
    public static long[][] matMul(long[][] l, long[][] r) throws IOException {
        int lh = l.length;
        int lw = l[0].length;
        int rh = r.length;
        int rw = r[0].length;
        //lwとrhが,同じである必要がある
        if (lw != rh) throw new IOException();
        long[][] res = new long[lh][rw];
        for (int i = 0; i < lh; i++) {
            for (int j = 0; j < rw; j++) {
                for (int k = 0; k < lw; k++) {
                    res[i][j] = modSum(res[i][j], modMul(l[i][k], r[k][j]));
                }
            }
        }
        return res;
    }

    public static long[][] matPow(long[][] a, int n) throws IOException {
        int h = a.length;
        int w = a[0].length;
        if (h != w) throw new IOException();
        long[][] res = new long[h][h];
        for (int i = 0; i < h; i++) {
            res[i][i] = 1;
        }
        long[][] pow = a.clone();
        while (n > 0) {
            if (bget(n, 0)) res = matMul(pow, res);
            pow = matMul(pow, pow);
            n >>= 1;
        }
        return res;
    }

    public static void chMax(long v) {
        maxRes = Math.max(maxRes, v);
    }

    public static void chMin(long v) {
        minRes = Math.min(minRes, v);
    }

    //便利系
    //左端、右端の情報をもたせる。
    public static void setLR(int[] a, ArrayList<Integer> l, ArrayList<Integer> r) {
        for (int i = 0; i < a.length; i++) {
            if (a[i] > 0) {
                int j = i;
                while (a[j] > 0) j++;
                l.add(i);
                r.add(j);
                i = j - 1;
            }
        }
    }

    public static int[] imosu(int[] f, int[] t, int n) {
        int[] imosu = new int[n + 1];
        for (int i = 0; i < f.length; i++) {
            imosu[f[i]]++;
            imosu[t[i] + 1]--;
        }
        for (int i = 0; i < n; i++) {
            imosu[i + 1] += imosu[i];
        }
        return imosu;
    }

    static int[] inverse(int[] a) {
        int[] res = new int[a.length];
        for (int i = 0; i < a.length; i++)
            res[a[i]] = i;
        return res;
    }

    //2点間の行き先を配列に持たせる
    static int[][] packE(int n, int[] from, int[] to) {
        int[][] g = new int[n][];
        int[] p = new int[n];
        for (int f : from)
            p[f]++;
        for (int t : to)
            p[t]++;
        for (int i = 0; i < n; i++)
            g[i] = new int[p[i]];
        for (int i = 0; i < from.length; i++) {
            g[from[i]][--p[from[i]]] = to[i];
            g[to[i]][--p[to[i]]] = from[i];
        }
        return g;
    }

    public static String notE(double v) {
        return BigDecimal.valueOf(v).toPlainString();
    }

    public static void print(char[][] a) {
        for (int i = 0; i < a.length; i++) {
            for (int j = 0; j < a[0].length; j++) {
                System.out.print(a[i][j]);
            }
            System.out.println("");
        }
    }

    public static <T> void print(ArrayList<T> a) {
        for (T t : a) {
            System.out.println(t);
        }
    }

    public static void print(int[] a) {
        for (int i = 0; i < a.length; i++)
            System.out.println(a[i]);
    }

    public static void print(long[] a) {
        for (int i = 0; i < a.length; i++)
            System.out.println(a[i]);
    }

    public static void print(int[][] a) {
        for (int i = 0; i < a.length; i++) {
            for (int j = 0; j < a[0].length; j++) {
                System.out.print(a[i][j]);
            }
            System.out.println("");
        }
    }

    //bit関連
    public static boolean bget(BitSet bit, int keta) {
        return bit.nextSetBit(keta) == keta;
    }

    public static boolean bget(long bit, int keta) {
        return ((bit >> keta) & 1) == 1;
    }


    public static int restoreHashA(long key) {
        return (int) (key >> 32);
    }

    public static int restoreHashB(long key) {
        return (int) (key & -1);
    }

    //正の数のみ
    public static long getHashKey(int a, int b) {
        return (long) a << 32 | b;
    }
    //数学関係--------------------------------

    //a/bを返す
    public static long ceil(long a, long b) {
        return (a % b == 0) ? a / b : a / b + 1;
    }

    public static long sqrt(long v) {
        long res = (long) Math.sqrt(v);
        while (res * res > v) res--;
        return res;
    }

    static long ncr2(int a, int b) {
        if (b == 0) return 1;
        else if (a < b) return 0;
        long res = 1;
        for (int i = 0; i < b; i++) {
            res *= a - i;
            res /= i + 1;
        }
        return res;
    }

    static double[][] PER_DP;

    static double ncrPer(int n, int r) {
        if (n < r) return 0;
        if (PER_DP == null) {
            PER_DP = new double[5001][5001];
            PER_DP[0][0] = 1;
            for (int ni = 0; ni < PER_DP.length - 1; ni++) {
                for (int ri = 0; ri < ni + 1; ri++) {
                    PER_DP[ni + 1][ri] += PER_DP[ni][ri] / 2;
                    PER_DP[ni + 1][ri + 1] += PER_DP[ni][ri] / 2;
                }
            }
        }
        return PER_DP[n][r];
    }

    public static int mod(int a, int m) {
        return a >= 0 ? a % m : (int) (a + ceil(-a, m) * m) % m;
    }

    static long modNcr(int n, int r) {
        if (n < 0 || r < 0 || n < r) return 0;
        if (Fa == null || Fa.size() <= n) factorial(n);
        long result = Fa.get(n);
        result = modMul(result, modInv(Fa.get(n - r)));
        result = modMul(result, modInv(Fa.get(r)));
        return result;
    }

    public static long modSum(long... lar) {
        long res = 0;
        for (long l : lar)
            res = (res + l % MOD) % MOD;
        if (res < 0) res += MOD;
        res %= MOD;
        return res;
    }

    public static long modDiff(long a, long b) {
        long res = a % MOD - b % MOD;
        if (res < 0) res += MOD;
        res %= MOD;
        return res;
    }

    public static long modMul(long... lar) {
        long res = 1;
        for (long l : lar)
            res = (res * l % MOD) % MOD;
        if (res < 0) res += MOD;
        res %= MOD;
        return res;
    }

    public static long modDiv(long... lar) {
        long res = lar[0] % MOD;
        for (int i = 1; i < lar.length; i++) {
            res = modMul(res, modInv(lar[i]));
        }
        return res;
    }

    static long modInv(long n) {
        return modPow(n, MOD - 2);
    }

    static void factorial(int n) {
        if (Fa == null) {
            Fa = new ArrayList<>();
            Fa.add(1L);
            Fa.add(1L);
        }
        for (int i = Fa.size(); i <= n; i++) {
            Fa.add((Fa.get(i - 1) * i) % MOD);
        }
    }

    static long modPow(long x, long n) {
        long res = 1L;
        while (n > 0) {
            if ((n & 1) == 1) {
                res = res * x % MOD;
            }
            x = x * x % MOD;
            n >>= 1;
        }
        return res;
    }

    //↑nCrをmod計算するために必要
    static long lcm(long n, long r) {
        return n / gcd(n, r) * r;
    }

    static int gcd(int n, int r) {
        return r == 0 ? n : gcd(r, n % r);
    }

    static long gcd(long n, long r) {
        return r == 0 ? n : gcd(r, n % r);
    }

    public static int u0(int a) {
        if (a < 0) return 0;
        return a;
    }

    public static long u0(long a) {
        if (a < 0) return 0;
        return a;
    }

    public static boolean[][] tbt(char[][] s, char c) {
        boolean[][] res = new boolean[s.length][s[0].length];
        for (int hi = 0; hi < s.length; hi++)
            for (int wi = 0; wi < s[0].length; wi++)
                if (s[hi][wi] == c) res[hi][wi] = true;
        return res;
    }

    public static int[] tia(int a) {
        int[] res = new int[keta(a)];
        for (int i = res.length - 1; i >= 0; i--) {
            res[i] = a % 10;
            a /= 10;
        }
        return res;
    }

    public static int[][] tit(char[][] a) {
        int[][] res = new int[a.length][a[0].length];
        for (int hi = 0; hi < a.length; hi++) {
            for (int wi = 0; wi < a[0].length; wi++) {
                res[hi][wi] = a[hi][wi] - '0';
            }
        }
        return res;
    }

    public static Integer[] toIntegerArray(int[] ar) {
        Integer[] res = new Integer[ar.length];
        for (int i = 0; i < ar.length; i++) {
            res[i] = ar[i];
        }
        return res;
    }

    public static long bitGetCombSizeK(int k) {
        return (1 << k) - 1;
    }

    //k個の次の組み合わせをビットで返す 大きさに上限はない 110110 -> 111001
    public static long bitNextComb(long comb) {
        long x = comb & -comb; //最下位の1
        long y = comb + x; //連続した下の1を繰り上がらせる
        return ((comb & ~y) / x >> 1) | y;
    }

    public static int keta(long num) {
        int res = 0;
        while (num > 0) {
            num /= 10;
            res++;
        }
        return res;
    }

    public static int ketaSum(long num) {
        int res = 0;
        while (num > 0) {
            res += num % 10;
            num /= 10;
        }
        return res;
    }

    public static boolean isOutofIndex(int x, int y, int w, int h) {
        if (x < 0 || y < 0) return true;
        if (w <= x || h <= y) return true;
        return false;
    }

    public static boolean isOutofIndex(int x, int y, char[][] ban) {
        if (x < 0 || y < 0) return true;
        if (ban[0].length <= x || ban.length <= y) return true;
        return false;
    }

    public static int arrayCount(int[] a, int v) {
        int res = 0;
        for (int i = 0; i < a.length; i++) {
            if (a[i] == v) res++;
        }
        return res;
    }

    public static int arrayCount(long[] a, int v) {
        int res = 0;
        for (int i = 0; i < a.length; i++) {
            if (a[i] == v) res++;
        }
        return res;
    }

    public static int arrayCount(int[][] a, int v) {
        int res = 0;
        for (int hi = 0; hi < a.length; hi++) {
            for (int wi = 0; wi < a[0].length; wi++) {
                if (a[hi][wi] == v) res++;
            }
        }
        return res;
    }

    public static int arrayCount(long[][] a, int v) {
        int res = 0;
        for (int hi = 0; hi < a.length; hi++) {
            for (int wi = 0; wi < a[0].length; wi++) {
                if (a[hi][wi] == v) res++;
            }
        }
        return res;
    }

    public static int arrayCount(char[][] a, char v) {
        int res = 0;
        for (int hi = 0; hi < a.length; hi++) {
            for (int wi = 0; wi < a[0].length; wi++) {
                if (a[hi][wi] == v) res++;
            }
        }
        return res;
    }

    public static void setPrimes() {
        int n = 100001;
        isPrime = new boolean[n];
        Arrays.fill(isPrime, true);
        isPrime[0] = isPrime[1] = false;
        for (int i = 2; i * i <= n; i++) {
            if (!isPrime[i]) continue;
            for (int j = i * 2; j < n; j += i) {
                isPrime[j] = false;
            }
        }
        primes = new ArrayList<>();
        for (int i = 2; i < n; i++) {
            if (isPrime[i]) primes.add(i);
        }
    }

    public static void revSort(int[] a) {
        Arrays.sort(a);
        reverse(a);
    }

    public static void revSort(long[] a) {
        Arrays.sort(a);
        reverse(a);
    }

    public static P[] clone(P[] ar) {
        P[] res = new P[ar.length];
        for (int i = 0; i < ar.length; i++) {
            res[i] = new P(ar[i].x, ar[i].y);
        }
        return res;
    }

    public static int[][] clone(int[][] ar) {
        int[][] nr = new int[ar.length][ar[0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                nr[i][j] = ar[i][j];
        return nr;
    }

    public static long[][] clone(long[][] ar) {
        long[][] nr = new long[ar.length][ar[0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                nr[i][j] = ar[i][j];
        return nr;
    }

    public static double[][] clone(double[][] ar) {
        double[][] nr = new double[ar.length][ar[0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                nr[i][j] = ar[i][j];
        return nr;
    }

    public static boolean[][] clone(boolean[][] ar) {
        boolean[][] nr = new boolean[ar.length][ar[0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                nr[i][j] = ar[i][j];
        return nr;
    }

    public static char[][] clone(char[][] ar) {
        char[][] nr = new char[ar.length][ar[0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                nr[i][j] = ar[i][j];
        return nr;
    }

    public static int[][][] clone(int[][][] ar) {
        int[][][] nr = new int[ar.length][ar[0].length][ar[0][0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                for (int k = 0; k < ar[0][0].length; k++)
                    nr[i][j][k] = ar[i][j][k];
        return nr;
    }

    public static long[][][] clone(long[][][] ar) {
        long[][][] nr = new long[ar.length][ar[0].length][ar[0][0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                for (int k = 0; k < ar[0][0].length; k++)
                    nr[i][j][k] = ar[i][j][k];
        return nr;
    }

    public static double[][][] clone(double[][][] ar) {
        double[][][] nr = new double[ar.length][ar[0].length][ar[0][0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                for (int k = 0; k < ar[0][0].length; k++)
                    nr[i][j][k] = ar[i][j][k];
        return nr;
    }

    public static boolean[][][] clone(boolean[][][] ar) {
        boolean[][][] nr = new boolean[ar.length][ar[0].length][ar[0][0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                for (int k = 0; k < ar[0][0].length; k++)
                    nr[i][j][k] = ar[i][j][k];
        return nr;
    }

    public static char[][][] clone(char[][][] ar) {
        char[][][] nr = new char[ar.length][ar[0].length][ar[0][0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                for (int k = 0; k < ar[0][0].length; k++)
                    nr[i][j][k] = ar[i][j][k];
        return nr;
    }

    /**
     * <h1>指定した値以上の先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値以上で、先頭になるインデクス
     * 値が無ければ、挿入できる最小のインデックス
     */
    public static <T extends Number> int lowerBound(final List<T> lis, final T value) {
        int low = 0;
        int high = lis.size();
        int mid;

        while (low < high) {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (lis.get(mid).doubleValue() < value.doubleValue()) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    //v未満で最大のiを返す。ただしvを満たすiがあるなら最小のiを返す
    public static <T extends Number> int rlowerBound(final List<T> lis, final T value) {
        int ind = lowerBound(lis, value);
        if (ind == lis.size() || !lis.get(ind).equals(value)) ind--;
        return ind;
    }

    /**
     * <h1>指定した値より大きい先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値より上で、先頭になるインデクス
     * 値が無ければ、挿入できる最小のインデックス
     */
    public static <T extends Number> int upperBound(final List<T> lis, final T value) {
        int low = 0;
        int high = lis.size();
        int mid;
        while (low < high) {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (lis.get(mid).doubleValue() < value.doubleValue()) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    public static int lowerBound(final int[] arr, final int value) {
        int low = 0;
        int high = arr.length;
        int mid;

        while (low < high) {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] < value) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    public static int rlowerBound(final int[] arr, final int value) {
        int ind = lowerBound(arr, value);
        if (ind == arr.length || arr[ind] != value) ind--;
        return ind;
    }


    public static int upperBound(final int[] arr, final int value) {
        int low = 0;
        int high = arr.length;
        int mid;
        while (low < high) {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] <= value) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    public static int lowerBound(final long[] arr, final long value) {
        int low = 0;
        int high = arr.length;
        int mid;
        while (low < high) {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] < value) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    public static int rlowerBound(final long[] arr, final long value) {
        int ind = lowerBound(arr, value);
        if (ind == arr.length || arr[ind] != value) ind--;
        return ind;
    }


    public static int upperBound(final long[] arr, final long value) {
        int low = 0;
        int high = arr.length;
        int mid;
        while (low < high) {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] <= value) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    //次の順列に書き換える、最大値ならfalseを返す
    public static boolean nextPermutation(int A[]) {
        int len = A.length;
        int pos = len - 2;
        for (; pos >= 0; pos--) {
            if (A[pos] < A[pos + 1]) break;
        }
        if (pos == -1) return false;

        //posより大きい最小の数を二分探索
        int ok = pos + 1;
        int ng = len;
        while (Math.abs(ng - ok) > 1) {
            int mid = (ok + ng) / 2;
            if (A[mid] > A[pos]) ok = mid;
            else ng = mid;

        }

        swap(A, pos, ok);
        reverse(A, pos + 1, len - 1);


        return true;
    }

    //次の順列に書き換える、最小値ならfalseを返す
    public static boolean prevPermutation(int A[]) {
        int len = A.length;
        int pos = len - 2;
        for (; pos >= 0; pos--) {
            if (A[pos] > A[pos + 1]) break;
        }
        if (pos == -1) return false;

        //posより小さい最大の数を二分探索
        int ok = pos + 1;
        int ng = len;
        while (Math.abs(ng - ok) > 1) {
            int mid = (ok + ng) / 2;
            if (A[mid] < A[pos]) ok = mid;
            else ng = mid;

        }

        swap(A, pos, ok);
        reverse(A, pos + 1, len - 1);


        return true;
    }


    static <T> void swap(T[] x, int i, int j) {
        T t = x[i];
        x[i] = x[j];
        x[j] = t;
    }

    static void swap(char[] x, int i, int j) {
        char t = x[i];
        x[i] = x[j];
        x[j] = t;
    }

    static void swap(int[] x, int i, int j) {
        int t = x[i];
        x[i] = x[j];
        x[j] = t;
    }

    public static String reverse(String a) {
        sb.append(a);
        String res = sb.reverse().toString();
        sb.setLength(0);
        return new String(res);
    }

    public static void reverse(int[] x) {
        int l = 0;
        int r = x.length - 1;
        while (l < r) {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    public static void reverse(long[] x) {
        int l = 0;
        int r = x.length - 1;
        while (l < r) {
            long temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    public static void reverse(char[] x) {
        int l = 0;
        int r = x.length - 1;
        while (l < r) {
            char temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    public static void reverse(int[] x, int s, int e) {
        int l = s;
        int r = e;
        while (l < r) {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    static int length(int a) {
        int cou = 0;
        while (a != 0) {
            a /= 10;
            cou++;
        }
        return cou;
    }

    static int length(long a) {
        int cou = 0;
        while (a != 0) {
            a /= 10;
            cou++;
        }
        return cou;
    }

    static int cou(boolean[] a) {
        int res = 0;
        for (boolean b : a) {
            if (b) res++;
        }
        return res;
    }

    static int cou(String s, char c) {
        int res = 0;
        for (char ci : s.toCharArray()) {
            if (ci == c) res++;
        }
        return res;
    }

    static int cou(char[][] a, char c) {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                if (a[i][j] == c) co++;
        return co;
    }

    static int cou(int[] a, int key) {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            if (a[i] == key) co++;
        return co;
    }

    static int cou(long[] a, long key) {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            if (a[i] == key) co++;
        return co;
    }

    static int cou(int[][] a, int key) {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                if (a[i][j] == key) co++;
        return co;
    }

    static void fill(int[][] a, int v) {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }

    static void fill(char[][] a, char c) {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = c;
    }

    static void fill(long[][] a, long v) {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }

    static void fill(boolean[][] a, boolean v) {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }

    static void fill(int[][][] a, int v) {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                for (int k = 0; k < a[0][0].length; k++)
                    a[i][j][k] = v;
    }

    static void fill(long[][][] a, long v) {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                for (int k = 0; k < a[0][0].length; k++)
                    a[i][j][k] = v;
    }

    static int max(int... a) {
        int res = Integer.MIN_VALUE;
        for (int i : a) {
            res = Math.max(res, i);
        }
        return res;
    }

    static long max(long... a) {
        long res = Integer.MIN_VALUE;
        for (long i : a) {
            res = Math.max(res, i);
        }
        return res;
    }

    static long min(long... a) {
        long res = Long.MAX_VALUE;
        for (long i : a) {
            res = Math.min(res, i);
        }
        return res;
    }

    static int max(int[][] ar) {
        int res = Integer.MIN_VALUE;
        for (int i[] : ar)
            res = Math.max(res, max(i));
        return res;
    }

    static long max(long[][] ar) {
        long res = Integer.MIN_VALUE;
        for (long i[] : ar)
            res = Math.max(res, max(i));
        return res;
    }

    static int min(int... a) {
        int res = Integer.MAX_VALUE;
        for (int i : a) {
            res = Math.min(res, i);
        }
        return res;
    }


    static int min(int[][] ar) {
        int res = Integer.MAX_VALUE;
        for (int i[] : ar)
            res = Math.min(res, min(i));
        return res;
    }

    public static <T extends Number> long sum(ArrayList<T> lis) {
        long res = 0;
        for (T li : lis) {
            res += li.longValue();
        }
        return res;
    }

    static long sum(int[] a) {
        long cou = 0;
        for (int i : a)
            cou += i;
        return cou;
    }

    static long sum(long[] a) {
        long cou = 0;
        for (long i : a)
            cou += i;
        return cou;
    }


    //FastScanner

    static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer tokenizer = null;

    public static String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    /*public String nextChar(){
        return (char)next()[0];
    }*/
    public static String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        return tokenizer.nextToken("\n");
    }

    public static long nl() {
        return Long.parseLong(next());
    }

    public static String n() {
        return next();
    }

    public static int ni() {
        return Integer.parseInt(next());
    }

    public static double nd() {
        return Double.parseDouble(next());
    }

    public static int[] nia(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        return a;
    }


    //1-index
    public static int[] niao(int n) {
        int[] a = new int[n + 1];
        for (int i = 1; i < n + 1; i++) {
            a[i] = ni();
        }
        return a;
    }

    //番兵法
    public static int[] nias(int n, int end) {
        int[] a = new int[n + 1];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        a[n] = end;
        return a;
    }

    public static int[] niad(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni() - 1;
        }
        return a;
    }

    public static P[] npa(int n) {
        P[] p = new P[n];
        for (int i = 0; i < n; i++) {
            p[i] = new P(ni(), ni());
        }
        return p;
    }

    public static P[] npad(int n) {
        P[] p = new P[n];
        for (int i = 0; i < n; i++) {
            p[i] = new P(ni() - 1, ni() - 1);
        }
        return p;
    }

    public static int[][] nit(int h, int w) {
        int[][] a = new int[h][w];
        for (int hi = 0; hi < h; hi++) {
            for (int wi = 0; wi < w; wi++) {
                a[hi][wi] = ni();
            }
        }
        return a;
    }

    public static int[][] nitd(int h, int w) {
        int[][] a = new int[h][w];
        for (int hi = 0; hi < h; hi++) {
            for (int wi = 0; wi < w; wi++) {
                a[hi][wi] = ni() - 1;
            }
        }
        return a;
    }

    static int[][] S_ARRAY;
    static long[][] S_LARRAY;
    static int S_INDEX;
    static int S_LINDEX;

    //複数の配列を受け取る
    public static int[] niah(int n, int k) throws Exception {
        if (S_ARRAY == null) {
            S_ARRAY = new int[k][n];
            for (int j = 0; j < n; j++) {
                for (int i = 0; i < k; i++) {
                    S_ARRAY[i][j] = ni();
                }
            }
        }
        return S_ARRAY[S_INDEX++];
    }

    public static long[] nlah(int n, int k) throws Exception {
        if (S_LARRAY == null) {
            S_LARRAY = new long[k][n];
            for (int j = 0; j < n; j++) {
                for (int i = 0; i < k; i++) {
                    S_LARRAY[i][j] = nl();
                }
            }
        }
        return S_LARRAY[S_LINDEX++];
    }

    //複数の配列を受け取る
    public static int[] niahd(int n, int k) throws Exception {
        if (S_ARRAY == null) {
            S_ARRAY = new int[k][n];
            for (int j = 0; j < n; j++) {
                for (int i = 0; i < k; i++) {
                    S_ARRAY[i][j] = ni();
                }
            }
        }
        for (int i = 0; i < N; i++)
            S_ARRAY[S_INDEX][i]--;
        return S_ARRAY[S_INDEX++];
    }

    public static long[] nlahd(int n, int k) throws Exception {
        if (S_LARRAY == null) {
            S_LARRAY = new long[k][n];
            for (int j = 0; j < n; j++) {
                for (int i = 0; i < k; i++) {
                    S_LARRAY[i][j] = nl() - 1;
                }
            }
        }
        return S_LARRAY[S_LINDEX++];
    }

    public static char[] nca() {
        char[] a = next().toCharArray();
        return a;
    }


    public static String[] nsa(int n) {
        String[] res = new String[n];
        for (int i = 0; i < n; i++) {
            res[i] = n();
        }
        return res;
    }

    //スペースが入っている場合
    public static char[][] ncts(int h, int w) {
        char[][] a = new char[h][w];
        for (int i = 0; i < h; i++) {
            a[i] = nextLine().replace(" ", "").toCharArray();
        }
        return a;
    }

    public static char[][] nct(int h, int w) {
        char[][] a = new char[h][w];
        for (int hi = 0; hi < h; hi++) {
            String s = nextLine();
            for (int wi = 0; wi < s.length(); wi++) {
                a[hi][wi] = s.charAt(wi);
            }
        }
        return a;
    }

    public static char[][] nctp(int h, int w, char c) {
        char[][] a = new char[h + 2][w + 2];
        for (int hi = 1; hi < h + 1; hi++) {
            String s = nextLine();
            for (int wi = 1; wi < s.length() + 1; wi++) {
                a[hi][wi] = s.charAt(wi - 1);
            }
        }
        for (int wi = 0; wi < w + 2; wi++)
            a[0][wi] = a[h + 1][wi] = c;
        for (int hi = 0; hi < h + 2; hi++)
            a[hi][0] = a[hi][w + 1] = c;
        return a;
    }

    //スペースが入ってる時用
    public static char[][] nctsp(int h, int w, char c) {
        char[][] a = new char[h + 2][w + 2];
        //char c = '*';
        int i;
        for (i = 0; i < w + 2; i++)
            a[0][i] = c;
        for (i = 1; i < h + 1; i++) {
            a[i] = (c + nextLine().replace(" ", "") + c).toCharArray();
        }
        for (i = 0; i < w + 2; i++)
            a[h + 1][i] = c;
        return a;
    }

    public static long[] nla(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nl();
        }
        return a;
    }

    public static long[] nlas(int n, long e) {
        long[] a = new long[n + 1];
        for (int i = 0; i < n; i++) {
            a[i] = nl();
        }
        a[n] = e;
        return a;
    }

    public static long[] nlao(int n) {
        long[] a = new long[n + 1];
        for (int i = 0; i < n; i++) {
            a[i + 1] = nl();
        }
        return a;
    }

    public static long[] nlad(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nl() - 1;
        }
        return a;
    }

    public static long[][] nlt(int h, int w) {
        long[][] a = new long[h][w];
        for (int hi = 0; hi < h; hi++) {
            for (int wi = 0; wi < w; wi++) {
                a[hi][wi] = nl();
            }
        }
        return a;
    }

    //便利クラス
    static class CouMap {
        public HashMap<Long, Long> map;
        public HashMap<String, Long> smap;

        CouMap() {
            map = new HashMap();
            smap = new HashMap();
        }

        public void put(long key, long value) {
            Long nowValue = map.get(key);
            map.put(key, nowValue == null ? value : nowValue + value);
        }

        public void put(String key, long value) {
            Long nowValue = smap.get(key);
            smap.put(key, nowValue == null ? value : nowValue + value);
        }

        public void mput(long key, long value) {
            Long nowValue = map.get(key);
            map.put(key, nowValue == null ? value % MOD : modSum(nowValue, value));
        }

        public void put(long key) {
            put(key, 1);
        }

        public void put(String key) {
            put(key, 1);
        }

        public void put(int... arg) {
            for (int i : arg) {
                put(i, 1);
            }
        }

        public void put(long... arg) {
            for (long i : arg) {
                put(i, 1);
            }
        }

        public void mput(int... arg) {
            for (int i : arg) {
                mput(i, 1);
            }
        }

        public void mput(long... arg) {
            for (long i : arg) {
                mput(i, 1);
            }
        }

        public long get(long key) {
            Long v = map.get(key);
            return v == null ? 0 : v;
        }

        public long get(String key) {
            Long v = map.get(key);
            return v == null ? 0 : v;
        }
    }

    static class P implements Comparable<P> {
        int x, y;

        @Override
        public int compareTo(P p) {
            //xyで昇順
            return x == p.x ? y - p.y : x - p.x;
            //xyで降順
            //return (x == p.x ? y - p.y : x - p.x) * -1;
            //yxで昇順
            //return y == p.y ? x - p.x : y - p.y;
            //yxで昇順
            //return (y == p.y ? x - p.x : y - p.y) * -1;

            //x昇 y降
            //return x == p.x ? p.y - y : x - p.x;
            //x降 y昇
            //return (x == p.x ? p.y - y : x - p.x) * -1;
            //y昇 x降
            //return y == p.y ? p.x - x : y - p.y;
            //y降 x昇
            //return (y == p.y ? p.x - x : y - p.y) * -1;
        }

        P(int a, int b) {
            x = a;
            y = b;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof P)) return false;
            P p = (P) o;
            return x == p.x && y == p.y;
        }

        @Override
        public int hashCode() {
            return Objects.hash(x, y);
        }

    }

    static class PL implements Comparable<PL> {
        long x, y;

        public int compareTo(PL p) {
            //xyで昇順
            long res = x == p.x ? y - p.y : x - p.x;
            //xyで降順
            //long res = (x == p.x ? y - p.y : x - p.x) * -1;
            //yxで昇順
            //long res = y == p.y ? x - p.x : y - p.y;
            //yxで昇順
            //long res = (y == p.y ? x - p.x : y - p.y) * -1;

            //x昇 y降
            //long res = x == p.x ? p.y - y : x - p.x;
            //x降 y昇
            //long res = (x == p.x ? p.y - y : x - p.x) * -1;
            //y昇 x降
            //long res = y == p.y ? p.x - x : y - p.y;
            //y降 x昇
            //long res = (y == p.y ? p.x - x : y - p.y) * -1;

            return (res == 0) ? 0 : res > 0 ? 1 : -1;
        }

        PL(long a, long b) {
            x = a;
            y = b;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof PL)) return false;
            PL p = (PL) o;
            return x == p.x && y == p.y;
        }

        @Override
        public int hashCode() {
            return Objects.hash(x, y);
        }

    }

    public static void main(String[] args) throws Exception {
        long startTime = System.currentTimeMillis();
        solve();
        System.out.flush();
        long endTime = System.currentTimeMillis();
        if (DEBUG) System.err.println(endTime - startTime);
    }

}