結果

問題 No.1634 Sorting Integers (Multiple of K) Hard
ユーザー 遭難者遭難者
提出日時 2021-07-16 15:57:02
言語 Java21
(openjdk 21)
結果
TLE  
(最新)
AC  
(最初)
実行時間 -
コード長 36,261 bytes
コンパイル時間 4,571 ms
コンパイル使用メモリ 102,872 KB
実行使用メモリ 94,484 KB
最終ジャッジ日時 2023-10-14 02:25:49
合計ジャッジ時間 56,006 ms
ジャッジサーバーID
(参考情報)
judge15 / judge12
このコードへのチャレンジ(β)

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 58 ms
50,488 KB
testcase_01 AC 59 ms
50,648 KB
testcase_02 AC 57 ms
50,356 KB
testcase_03 AC 121 ms
55,336 KB
testcase_04 AC 133 ms
57,088 KB
testcase_05 AC 1,663 ms
83,448 KB
testcase_06 AC 1,491 ms
82,060 KB
testcase_07 AC 1,665 ms
82,952 KB
testcase_08 AC 1,685 ms
87,440 KB
testcase_09 AC 60 ms
50,696 KB
testcase_10 AC 59 ms
50,848 KB
testcase_11 AC 2,014 ms
93,488 KB
testcase_12 AC 1,946 ms
87,292 KB
testcase_13 AC 2,106 ms
93,076 KB
testcase_14 TLE -
testcase_15 AC 2,328 ms
88,040 KB
testcase_16 AC 2,009 ms
91,364 KB
testcase_17 AC 1,873 ms
90,376 KB
testcase_18 AC 1,305 ms
83,660 KB
testcase_19 AC 2,475 ms
92,064 KB
testcase_20 AC 1,112 ms
86,360 KB
testcase_21 AC 643 ms
76,844 KB
testcase_22 AC 1,848 ms
89,880 KB
testcase_23 AC 2,110 ms
94,484 KB
testcase_24 AC 1,913 ms
87,912 KB
testcase_25 AC 1,871 ms
89,064 KB
testcase_26 AC 1,700 ms
90,620 KB
testcase_27 AC 2,608 ms
91,764 KB
testcase_28 AC 1,529 ms
83,064 KB
testcase_29 AC 2,504 ms
88,672 KB
testcase_30 AC 1,474 ms
83,996 KB
testcase_31 AC 1,511 ms
83,356 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

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

class Main {
    private static void solve() {
        int n = sc.nextInt();
        long k = sc.nextLong();
        var ka = new long[16];
        ka[0] = 1;
        for (int i = 1; i < 16; i++)
            ka[i] = i * ka[i - 1];
        var a = new int[n];
        int cn = 0;
        for (int i = 0; i < 9; i++) {
            int nc = sc.nextInt();
            for (int j = 0; j < nc; j++)
                a[cn++] = i + 1;
        }
        if (n < 7) {
            var r = new HashSet<Long>();
            for (var i : new Permutation(n)) {
                long s = 0;
                for (int j : i) {
                    s *= 10;
                    s += a[j];
                }
                if (s % k == 0)
                    r.add(s);
            }
            ou.println(r.size());
            return;
        }
        int nn = n >> 1, mm = n - nn;
        int ma = 1 << n;
        long m10 = mp(10, mm, k);
        var aa = new HashMap<Long, Long>();
        var bb = new HashMap<Long, Long>();
        var xx = new HashSet<String>();
        var aaa = new int[nn];
        var bbb = new int[mm];
        long ans = 0;
        var tt = new int[9];
        for (int bi = (1 << nn) - 1; bi < ma; bi = n(bi)) {
            aa.clear();
            bb.clear();
            int ii = bi;
            int cc = 0;
            int ccc = 0;
            var ss = new StringBuilder();
            for (int i = 0; i < n; i++) {
                if ((ii & 1) == 1) {
                    aaa[cc] = a[i];
                    ss.append(String.valueOf(aaa[cc]));
                    cc++;
                } else {
                    bbb[ccc] = a[i];
                    ccc++;
                }
                ii >>= 1;
            }
            var rr = ss.toString();
            if (xx.contains(rr))
                continue;
            xx.add(rr);
            for (var i : new Permutation(nn)) {
                long s = 0;
                for (int j : i) {
                    s *= 10;
                    s += aaa[j];
                }
                s *= m10;
                s %= k;
                if (aa.containsKey(s))
                    aa.put(s, aa.get(s) + 1L);
                else
                    aa.put(s, 1L);
            }
            for (var i : new Permutation(mm)) {
                long s = 0;
                for (int j : i) {
                    s *= 10;
                    s += bbb[j];
                }
                s = -s;
                s %= k;
                if (s < 0)
                    s += k;
                if (bb.containsKey(s))
                    bb.put(s, bb.get(s) + 1L);
                else
                    bb.put(s, 1L);
            }
            var r = new A();
            aa.forEach((i, j) -> {
                if (bb.containsKey(i))
                    r.a(j * bb.get(i));
            });
            long tr = r.a;
            Arrays.fill(tt, 0);
            for (int i : aaa)
                tt[i - 1]++;
            for (int i : tt)
                tr /= ka[i];
            Arrays.fill(tt, 0);
            for (int i : bbb)
                tt[i - 1]++;
            for (int i : tt)
                tr /= ka[i];
            ans += tr;
        }
        ou.println(ans);
    }

    private static long mp(long a, long b, long m) {
        if (b == 0)
            return 1;
        if ((b & 1) == 1)
            return (a * mp(a, b - 1, m)) % m;
        return mp((a * a) % m, b >> 1, m);
    }

    private static int n(int s) {
        int x = s & -s, y = s + x;
        return (((s & ~y) / x) >> 1) | y;
    }

    public static void main(String[] args) {
        solve();
        ou.flush();
        ou.close();
    }

    private static ContestScanner sc = new ContestScanner();
    private static ContestPrinter ou = new ContestPrinter();
}

class A {
    long a = 0L;

    public void a(long x) {
        a += x;
    }

    public void d(long x) {
        a /= x;
    }

    public long g() {
        return a;
    }

    @Override
    public String toString() {
        return String.valueOf(a);
    }
}

class Permutation implements java.util.Iterator<int[]>, Iterable<int[]> {
    private int[] next;

    public Permutation(int n) {
        next = java.util.stream.IntStream.range(0, n).toArray();
    }

    @Override
    public boolean hasNext() {
        return next != null;
    }

    @Override
    public int[] next() {
        int[] r = next.clone();
        next = nextPermutation(next);
        return r;
    }

    @Override
    public java.util.Iterator<int[]> iterator() {
        return this;
    }

    public static int[] nextPermutation(int[] a) {
        if (a == null || a.length < 2)
            return null;
        int p = 0;
        for (int i = a.length - 2; i >= 0; i--) {
            if (a[i] >= a[i + 1])
                continue;
            p = i;
            break;
        }
        int q = 0;
        for (int i = a.length - 1; i > p; i--) {
            if (a[i] <= a[p])
                continue;
            q = i;
            break;
        }
        if (p == 0 && q == 0)
            return null;
        int temp = a[p];
        a[p] = a[q];
        a[q] = temp;
        int l = p, r = a.length;
        while (++l < --r) {
            temp = a[l];
            a[l] = a[r];
            a[r] = temp;
        }
        return a;
    }
}

class ModIntFactory {
    private final ModArithmetic ma;
    private final int mod;

    private final boolean usesMontgomery;
    private final ModArithmetic.ModArithmeticMontgomery maMontgomery;

    private ArrayList<Integer> factorial;

    public ModIntFactory(int mod) {
        this.ma = ModArithmetic.of(mod);
        this.usesMontgomery = ma instanceof ModArithmetic.ModArithmeticMontgomery;
        this.maMontgomery = usesMontgomery ? (ModArithmetic.ModArithmeticMontgomery) ma : null;
        this.mod = mod;

        this.factorial = new ArrayList<>();
    }

    public ModIntFactory(double mod) {
        this((int) mod);
    }

    public ModInt create(long value) {
        if ((value %= mod) < 0)
            value += mod;
        if (usesMontgomery) {
            return new ModInt(maMontgomery.generate(value));
        } else {
            return new ModInt((int) value);
        }
    }

    private void prepareFactorial(int max) {
        factorial.ensureCapacity(max + 1);
        if (factorial.size() == 0)
            factorial.add(1);
        for (int i = factorial.size(); i <= max; i++) {
            if (usesMontgomery)
                factorial.add(ma.mul(factorial.get(i - 1), maMontgomery.generate(i)));
            else
                factorial.add(ma.mul(factorial.get(i - 1), i));
        }
    }

    public ModInt factorial(int i) {
        prepareFactorial(i);
        return create(factorial.get(i));
    }

    public ModInt permutation(int n, int r) {
        if (n < 0 || r < 0 || n < r)
            return create(0);
        prepareFactorial(n);
        return create(ma.div(factorial.get(n), factorial.get(r)));
    }

    public ModInt combination(int n, int r) {
        if (n < 0 || r < 0 || n < r)
            return create(0);
        prepareFactorial(n);
        return create(ma.div(factorial.get(n), ma.mul(factorial.get(r), factorial.get(n - r))));
    }

    public int getMod() {
        return mod;
    }

    public class ModInt {
        private int value;

        private ModInt(int value) {
            this.value = value;
        }

        public int mod() {
            return mod;
        }

        public int value() {
            if (usesMontgomery) {
                return maMontgomery.reduce(value);
            }
            return value;
        }

        public ModInt add(ModInt mi) {
            return new ModInt(ma.add(value, mi.value));
        }

        public ModInt add(ModInt mi1, ModInt mi2) {
            return new ModInt(ma.add(value, mi1.value)).addAsg(mi2);
        }

        public ModInt add(ModInt mi1, ModInt mi2, ModInt mi3) {
            return new ModInt(ma.add(value, mi1.value)).addAsg(mi2).addAsg(mi3);
        }

        public ModInt add(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
            return new ModInt(ma.add(value, mi1.value)).addAsg(mi2).addAsg(mi3).addAsg(mi4);
        }

        public ModInt add(ModInt mi1, ModInt... mis) {
            ModInt mi = add(mi1);
            for (ModInt m : mis)
                mi.addAsg(m);
            return mi;
        }

        public ModInt add(long mi) {
            return new ModInt(ma.add(value, ma.remainder(mi)));
        }

        public ModInt sub(ModInt mi) {
            return new ModInt(ma.sub(value, mi.value));
        }

        public ModInt sub(long mi) {
            return new ModInt(ma.sub(value, ma.remainder(mi)));
        }

        public ModInt mul(ModInt mi) {
            return new ModInt(ma.mul(value, mi.value));
        }

        public ModInt mul(ModInt mi1, ModInt mi2) {
            return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2);
        }

        public ModInt mul(ModInt mi1, ModInt mi2, ModInt mi3) {
            return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2).mulAsg(mi3);
        }

        public ModInt mul(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
            return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2).mulAsg(mi3).mulAsg(mi4);
        }

        public ModInt mul(ModInt mi1, ModInt... mis) {
            ModInt mi = mul(mi1);
            for (ModInt m : mis)
                mi.mulAsg(m);
            return mi;
        }

        public ModInt mul(long mi) {
            return new ModInt(ma.mul(value, ma.remainder(mi)));
        }

        public ModInt div(ModInt mi) {
            return new ModInt(ma.div(value, mi.value));
        }

        public ModInt div(long mi) {
            return new ModInt(ma.div(value, ma.remainder(mi)));
        }

        public ModInt inv() {
            return new ModInt(ma.inv(value));
        }

        public ModInt pow(long b) {
            return new ModInt(ma.pow(value, b));
        }

        public ModInt pow(ModInt mi) {
            return new ModInt(ma.pow(value, mi.value));
        }

        public ModInt addAsg(ModInt mi) {
            this.value = ma.add(value, mi.value);
            return this;
        }

        public ModInt addAsg(ModInt mi1, ModInt mi2) {
            return addAsg(mi1).addAsg(mi2);
        }

        public ModInt addAsg(ModInt mi1, ModInt mi2, ModInt mi3) {
            return addAsg(mi1).addAsg(mi2).addAsg(mi3);
        }

        public ModInt addAsg(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
            return addAsg(mi1).addAsg(mi2).addAsg(mi3).addAsg(mi4);
        }

        public ModInt addAsg(ModInt... mis) {
            for (ModInt m : mis)
                addAsg(m);
            return this;
        }

        public ModInt addAsg(long mi) {
            this.value = ma.add(value, ma.remainder(mi));
            return this;
        }

        public ModInt subAsg(ModInt mi) {
            this.value = ma.sub(value, mi.value);
            return this;
        }

        public ModInt subAsg(long mi) {
            this.value = ma.sub(value, ma.remainder(mi));
            return this;
        }

        public ModInt mulAsg(ModInt mi) {
            this.value = ma.mul(value, mi.value);
            return this;
        }

        public ModInt mulAsg(ModInt mi1, ModInt mi2) {
            return mulAsg(mi1).mulAsg(mi2);
        }

        public ModInt mulAsg(ModInt mi1, ModInt mi2, ModInt mi3) {
            return mulAsg(mi1).mulAsg(mi2).mulAsg(mi3);
        }

        public ModInt mulAsg(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
            return mulAsg(mi1).mulAsg(mi2).mulAsg(mi3).mulAsg(mi4);
        }

        public ModInt mulAsg(ModInt... mis) {
            for (ModInt m : mis)
                mulAsg(m);
            return this;
        }

        public ModInt mulAsg(long mi) {
            this.value = ma.mul(value, ma.remainder(mi));
            return this;
        }

        public ModInt divAsg(ModInt mi) {
            this.value = ma.div(value, mi.value);
            return this;
        }

        public ModInt divAsg(long mi) {
            this.value = ma.div(value, ma.remainder(mi));
            return this;
        }

        public ModInt powAsg(ModInt mi) {
            this.value = ma.pow(value, mi.value);
            return this;
        }

        public ModInt powAsg(long mi) {
            this.value = ma.pow(value, ma.remainder(mi));
            return this;
        }

        @Override
        public String toString() {
            return String.valueOf(value());
        }

        @Override
        public boolean equals(Object o) {
            if (o instanceof ModInt) {
                ModInt mi = (ModInt) o;
                return mod() == mi.mod() && value() == mi.value();
            }
            return false;
        }

        @Override
        public int hashCode() {
            return (1 * 37 + mod()) * 37 + value();
        }
    }

    private static abstract class ModArithmetic {
        abstract int mod();

        abstract int remainder(long value);

        abstract int add(int a, int b);

        abstract int sub(int a, int b);

        abstract int mul(int a, int b);

        int div(int a, int b) {
            return mul(a, inv(b));
        }

        int inv(int a) {
            int b = mod();
            if (b == 1)
                return 0;
            long u = 1, v = 0;
            while (b >= 1) {
                int t = a / b;
                a -= t * b;
                int tmp1 = a;
                a = b;
                b = tmp1;
                u -= t * v;
                long tmp2 = u;
                u = v;
                v = tmp2;
            }
            if (a != 1)
                throw new ArithmeticException("divide by zero");
            return remainder(u);
        }

        int pow(int a, long b) {
            if (b < 0)
                throw new ArithmeticException("negative power");
            int r = 1;
            int x = a;
            while (b > 0) {
                if ((b & 1) == 1)
                    r = mul(r, x);
                x = mul(x, x);
                b >>= 1;
            }
            return r;
        }

        static ModArithmetic of(int mod) {
            if (mod <= 0) {
                throw new IllegalArgumentException();
            } else if (mod == 1) {
                return new ModArithmetic1();
            } else if (mod == 2) {
                return new ModArithmetic2();
            } else if (mod == 998244353) {
                return new ModArithmetic998244353();
            } else if (mod == 1000000007) {
                return new ModArithmetic1000000007();
            } else if ((mod & 1) == 1) {
                return new ModArithmeticMontgomery(mod);
            } else {
                return new ModArithmeticBarrett(mod);
            }
        }

        private static final class ModArithmetic1 extends ModArithmetic {
            int mod() {
                return 1;
            }

            int remainder(long value) {
                return 0;
            }

            int add(int a, int b) {
                return 0;
            }

            int sub(int a, int b) {
                return 0;
            }

            int mul(int a, int b) {
                return 0;
            }

            int pow(int a, long b) {
                return 0;
            }
        }

        private static final class ModArithmetic2 extends ModArithmetic {
            int mod() {
                return 2;
            }

            int remainder(long value) {
                return (int) (value & 1);
            }

            int add(int a, int b) {
                return a ^ b;
            }

            int sub(int a, int b) {
                return a ^ b;
            }

            int mul(int a, int b) {
                return a & b;
            }
        }

        private static final class ModArithmetic998244353 extends ModArithmetic {
            private final int mod = 998244353;

            int mod() {
                return mod;
            }

            int remainder(long value) {
                return (int) ((value %= mod) < 0 ? value + mod : value);
            }

            int add(int a, int b) {
                int res = a + b;
                return res >= mod ? res - mod : res;
            }

            int sub(int a, int b) {
                int res = a - b;
                return res < 0 ? res + mod : res;
            }

            int mul(int a, int b) {
                return (int) (((long) a * b) % mod);
            }
        }

        private static final class ModArithmetic1000000007 extends ModArithmetic {
            private final int mod = 1000000007;

            int mod() {
                return mod;
            }

            int remainder(long value) {
                return (int) ((value %= mod) < 0 ? value + mod : value);
            }

            int add(int a, int b) {
                int res = a + b;
                return res >= mod ? res - mod : res;
            }

            int sub(int a, int b) {
                int res = a - b;
                return res < 0 ? res + mod : res;
            }

            int mul(int a, int b) {
                return (int) (((long) a * b) % mod);
            }
        }

        private static final class ModArithmeticMontgomery extends ModArithmeticDynamic {
            private final long negInv;
            private final long r2;

            private ModArithmeticMontgomery(int mod) {
                super(mod);
                long inv = 0;
                long s = 1, t = 0;
                for (int i = 0; i < 32; i++) {
                    if ((t & 1) == 0) {
                        t += mod;
                        inv += s;
                    }
                    t >>= 1;
                    s <<= 1;
                }
                long r = (1l << 32) % mod;
                this.negInv = inv;
                this.r2 = (r * r) % mod;
            }

            private int generate(long x) {
                return reduce(x * r2);
            }

            private int reduce(long x) {
                x = (x + ((x * negInv) & 0xffff_ffffl) * mod) >>> 32;
                return (int) (x < mod ? x : x - mod);
            }

            @Override
            int remainder(long value) {
                return generate((value %= mod) < 0 ? value + mod : value);
            }

            @Override
            int mul(int a, int b) {
                return reduce((long) a * b);
            }

            @Override
            int inv(int a) {
                return super.inv(reduce(a));
            }

            @Override
            int pow(int a, long b) {
                return generate(super.pow(a, b));
            }
        }

        private static final class ModArithmeticBarrett extends ModArithmeticDynamic {
            private static final long mask = 0xffff_ffffl;
            private final long mh;
            private final long ml;

            private ModArithmeticBarrett(int mod) {
                super(mod);
                long a = (1l << 32) / mod;
                long b = (1l << 32) % mod;
                long m = a * a * mod + 2 * a * b + (b * b) / mod;
                mh = m >>> 32;
                ml = m & mask;
            }

            private int reduce(long x) {
                long z = (x & mask) * ml;
                z = (x & mask) * mh + (x >>> 32) * ml + (z >>> 32);
                z = (x >>> 32) * mh + (z >>> 32);
                x -= z * mod;
                return (int) (x < mod ? x : x - mod);
            }

            @Override
            int remainder(long value) {
                return (int) ((value %= mod) < 0 ? value + mod : value);
            }

            @Override
            int mul(int a, int b) {
                return reduce((long) a * b);
            }
        }

        private static class ModArithmeticDynamic extends ModArithmetic {
            final int mod;

            ModArithmeticDynamic(int mod) {
                this.mod = mod;
            }

            int mod() {
                return mod;
            }

            int remainder(long value) {
                return (int) ((value %= mod) < 0 ? value + mod : value);
            }

            int add(int a, int b) {
                int sum = a + b;
                return sum >= mod ? sum - mod : sum;
            }

            int sub(int a, int b) {
                int sum = a - b;
                return sum < 0 ? sum + mod : sum;
            }

            int mul(int a, int b) {
                return (int) (((long) a * b) % mod);
            }
        }
    }
}

class ContestScanner {
    private final InputStream in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    public ContestScanner(InputStream in) {
        this.in = in;
    }

    public ContestScanner() {
        this(System.in);
    }

    private boolean hasNextByte() {
        if (ptr < buflen)
            return true;
        ptr = 0;
        try {
            buflen = in.read(buffer);
        } catch (IOException e) {
            e.printStackTrace();
        }
        return buflen > 0;
    }

    private int readByte() {
        return hasNextByte() ? buffer[ptr++] : -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public void nextThrow(int n) {
        for (int i = 0; i < n; i++)
            this.next();
    }

    public void nextThrow() {
        this.nextThrow(1);
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b)
            throw new NumberFormatException();
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b))
                return minus ? -n : n;
            else
                throw new NumberFormatException();
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

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

    public boolean[] nextBoolean(char True) {
        String s = this.next();
        int n = s.length();
        boolean[] array = new boolean[n];
        for (int i = 0; i < n; i++)
            array[i] = s.charAt(i) == True;
        return array;
    }

    public long[] nextLongArray(int length) {
        long[] array = new long[length];
        for (int i = 0; i < length; i++)
            array[i] = this.nextLong();
        return array;
    }

    public long[] nextLongArray(int length, java.util.function.LongUnaryOperator map) {
        long[] array = new long[length];
        for (int i = 0; i < length; i++)
            array[i] = map.applyAsLong(this.nextLong());
        return array;
    }

    public long[] nextLongArray(int length, long[] a) {
        long[] array = new long[length + a.length];
        for (int i = 0; i < length; i++)
            array[i] = this.nextLong();
        for (int i = length; i < array.length; i++)
            array[i] = a[i - length];
        return array;
    }

    public int[] nextIntArray(int length) {
        int[] array = new int[length];
        for (int i = 0; i < length; i++)
            array[i] = this.nextInt();
        return array;
    }

    public int[] nextIntArray(int length, java.util.function.IntUnaryOperator map) {
        int[] array = new int[length];
        for (int i = 0; i < length; i++)
            array[i] = map.applyAsInt(this.nextInt());
        return array;
    }

    public int[] nextIntArray(int length, int[] array) {
        int n = length + array.length;
        int[] a = new int[n];
        for (int i = 0; i < length; i++)
            a[i] = this.nextInt();
        for (int i = length; i < n; i++)
            a[i] = array[i - length];
        return a;
    }

    public Integer[] nextIntegerArray(int length, java.util.function.IntUnaryOperator map) {
        Integer[] array = new Integer[length];
        for (int i = 0; i < length; i++)
            array[i] = map.applyAsInt(this.nextInt());
        return array;
    }

    public Integer[] nextIntegerArray(int length) {
        Integer[] array = new Integer[length];
        for (int i = 0; i < length; i++)
            array[i] = this.nextInt();
        return array;
    }

    public double[] nextDoubleArray(int length) {
        double[] array = new double[length];
        for (int i = 0; i < length; i++)
            array[i] = this.nextDouble();
        return array;
    }

    public double[] nextDoubleArray(int length, java.util.function.DoubleUnaryOperator map) {
        double[] array = new double[length];
        for (int i = 0; i < length; i++)
            array[i] = map.applyAsDouble(this.nextDouble());
        return array;
    }

    public String[] nextArray(int length) {
        String[] array = new String[length];
        for (int i = 0; i < length; i++)
            array[i] = this.next();
        return array;
    }

    public long[][] nextLongMatrix(int height, int width) {
        long[][] mat = new long[height][width];
        for (int h = 0; h < height; h++)
            for (int w = 0; w < width; w++)
                mat[h][w] = this.nextLong();
        return mat;
    }

    public int[][] nextIntMatrix(int height, int width) {
        int[][] mat = new int[height][width];
        for (int h = 0; h < height; h++)
            for (int w = 0; w < width; w++)
                mat[h][w] = this.nextInt();
        return mat;
    }

    public int[][] nextIntMatrix(int height, int width, java.util.function.IntUnaryOperator map) {
        int[][] mat = new int[height][width];
        for (int h = 0; h < height; h++)
            for (int w = 0; w < width; w++)
                mat[h][w] = map.applyAsInt(this.nextInt());
        return mat;
    }

    public double[][] nextDoubleMatrix(int height, int width) {
        double[][] mat = new double[height][width];
        for (int h = 0; h < height; h++)
            for (int w = 0; w < width; w++)
                mat[h][w] = this.nextDouble();
        return mat;
    }

    public boolean[][] nextBooleanMatrix(int height, int width, char True) {
        boolean[][] mat = new boolean[height][width];
        for (int h = 0; h < height; h++) {
            String s = this.next();
            for (int w = 0; w < width; w++)
                mat[h][w] = s.charAt(w) == True;
        }
        return mat;
    }

    public char[][] nextCharMatrix(int height, int width) {
        char[][] mat = new char[height][width];
        for (int h = 0; h < height; h++) {
            String s = this.next();
            for (int w = 0; w < width; w++)
                mat[h][w] = s.charAt(w);
        }
        return mat;
    }

    public char[][] nextCharMatrix(int height, int width, int h, int w, char c) {
        char[][] mat = new char[height + 2 * h][width + 2 * w];
        for (int i = 0; i < height; i++) {
            String s = this.next();
            for (int j = 0; j < width; j++)
                mat[i + h][j + w] = s.charAt(j);
        }
        for (int i = 0; i < h; i++)
            for (int j = 0; j < 2 * w + width; j++)
                mat[i][j] = c;
        for (int i = h + height; i < 2 * h + height; i++)
            for (int j = 0; j < 2 * w + width; j++)
                mat[i][j] = c;
        for (int i = h; i < h + height; i++) {
            for (int j = 0; j < w; j++)
                mat[i][j] = c;
            for (int j = w + width; j < 2 * w + width; j++)
                mat[i][j] = c;
        }
        return mat;
    }

    public boolean[][] nextBooleanMatrix(int height, int width, int h, int w, char c) {
        boolean[][] mat = new boolean[height + 2 * h][width + 2 * w];
        for (int i = 0; i < height; i++) {
            String s = this.next();
            for (int j = 0; j < width; j++)
                mat[i + h][j + w] = s.charAt(j) == c;
        }
        return mat;
    }
}

class ContestPrinter extends PrintWriter {
    public ContestPrinter(PrintStream stream) {
        super(stream);
    }

    public ContestPrinter() {
        super(System.out);
    }

    private static String dtos(double x, int n) {
        StringBuilder sb = new StringBuilder();
        if (x < 0) {
            sb.append('-');
            x = -x;
        }
        x += Math.pow(10, -n) / 2;
        sb.append((long) x);
        sb.append(".");
        x -= (long) x;
        for (int i = 0; i < n; i++) {
            x *= 10;
            sb.append((int) x);
            x -= (int) x;
        }
        return sb.toString();
    }

    @Override
    public void print(float f) {
        super.print(dtos(f, 20));
    }

    @Override
    public void println(float f) {
        super.println(dtos(f, 20));
    }

    @Override
    public void print(double d) {
        super.print(dtos(d, 20));
    }

    @Override
    public void println(double d) {
        super.println(dtos(d, 20));
    }

    public void printlnArray(String[] array) {
        for (String i : array)
            super.println(i);
    }

    public void printSpace(Object... o) {
        int n = o.length - 1;
        for (int i = 0; i < n; i++) {
            super.print(o[i]);
            super.print(" ");
        }
        super.println(o[n]);
    }

    public void println(Object... o) {
        int n = o.length - 1;
        for (int i = 0; i < n; i++)
            super.print(o[i]);
        super.println(o[n]);
    }

    public void printYN(boolean o) {
        super.println(o ? "Yes" : "No");
    }

    public void print(Object... o) {
        int n = o.length - 1;
        for (int i = 0; i < n; i++)
            super.print(o[i]);
        super.print(o[n]);
    }

    public void printArray(Object[] array) {
        int n = array.length - 1;
        for (int i = 0; i < n; i++) {
            super.print(array[i]);
            super.print(" ");
        }
        super.println(array[n]);
    }

    public void printArray(int[] array, String separator) {
        int n = array.length - 1;
        for (int i = 0; i < n; i++) {
            super.print(array[i]);
            super.print(separator);
        }
        super.println(array[n]);
    }

    public void printArray(int[] array) {
        this.printArray(array, " ");
    }

    public void printArray(Integer[] array) {
        this.printArray(array, " ");
    }

    public void printArray(Integer[] array, String separator) {
        int n = array.length - 1;
        for (int i = 0; i < n; i++) {
            super.print(array[i]);
            super.print(separator);
        }
        super.println(array[n]);
    }

    public void printlnArray(int[] array) {
        for (int i : array)
            super.println(i);
    }

    public void printArray(int[] array, String separator, java.util.function.IntUnaryOperator map) {
        int n = array.length - 1;
        for (int i = 0; i < n; i++) {
            super.print(map.applyAsInt(array[i]));
            super.print(separator);
        }
        super.println(map.applyAsInt(array[n]));
    }

    public void printlnArray(int[] array, java.util.function.IntUnaryOperator map) {
        for (int i : array)
            super.println(map.applyAsInt(i));
    }

    public void printlnArray(long[] array, java.util.function.LongUnaryOperator map) {
        for (long i : array)
            super.println(map.applyAsLong(i));
    }

    public void printArray(int[] array, java.util.function.IntUnaryOperator map) {
        this.printArray(array, " ", map);
    }

    public void printArray(long[] array, String separator) {
        int n = array.length - 1;
        for (int i = 0; i < n; i++) {
            super.print(array[i]);
            super.print(separator);
        }
        super.println(array[n]);
    }

    public void printArray(long[] array) {
        this.printArray(array, " ");
    }

    public void printlnArray(long[] array) {
        for (long i : array)
            super.println(i);
    }

    public void printArray(double[] array) {
        printArray(array, " ");
    }

    public void printArray(double[] array, String separator) {
        int n = array.length - 1;
        for (int i = 0; i < n; i++) {
            super.print(array[i]);
            super.print(separator);
        }
        super.println(array[n]);
    }

    public void printlnArray(double[] array) {
        for (double i : array)
            super.println(i);
    }

    public void printArray(boolean[] array, String a, String b) {
        int n = array.length - 1;
        for (int i = 0; i < n; i++)
            super.print((array[i] ? a : b) + " ");
        super.println(array[n] ? a : b);
    }

    public void printArray(boolean[] array) {
        this.printArray(array, "Y", "N");
    }

    public void printArray(long[] array, String separator, java.util.function.LongUnaryOperator map) {
        int n = array.length - 1;
        for (int i = 0; i < n; i++) {
            super.print(map.applyAsLong(array[i]));
            super.print(separator);
        }
        super.println(map.applyAsLong(array[n]));
    }

    public void printArray(long[] array, java.util.function.LongUnaryOperator map) {
        this.printArray(array, " ", map);
    }

    public void printArray(ArrayList<?> array) {
        this.printArray(array, " ");
    }

    public void printArray(ArrayList<?> array, String separator) {
        int n = array.size() - 1;
        if (n == -1)
            return;
        for (int i = 0; i < n; i++) {
            super.print(array.get(i).toString());
            super.print(separator);
        }
        super.println(array.get(n).toString());
    }

    public void printlnArray(ArrayList<?> array) {
        int n = array.size();
        for (int i = 0; i < n; i++)
            super.println(array.get(i).toString());
    }

    public void printArray(int[][] array) {
        int n = array.length;
        if (n == 0)
            return;
        int m = array[0].length - 1;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++)
                super.print(array[i][j] + " ");
            super.println(array[i][m]);
        }
    }

    public void printArray(long[][] array) {
        int n = array.length;
        if (n == 0)
            return;
        int m = array[0].length - 1;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++)
                super.print(array[i][j] + " ");
            super.println(array[i][m]);
        }
    }

    public void printArray(boolean[][] array) {
        int n = array.length;
        if (n == 0)
            return;
        int m = array[0].length - 1;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++)
                super.print(array[i][j] ? "○ " : "× ");
            super.println(array[i][m] ? "○" : "×");
        }
    }

    public void printArray(char[][] array) {
        int n = array.length;
        if (n == 0)
            return;
        int m = array[0].length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++)
                super.print(array[i][j]);
            super.println();
        }
    }
}
0