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

public class Main {
    public static void solve(ContestScanner sc, ContestPrinter ou) {
        long u = (long) 5e18;
        int n = sc.nextInt();
        int m = sc.nextInt();
        int k = sc.nextInt();
        var g = new ArrayList<ArrayList<Point>>();
        var d = new DSU(n);
        for (int i = 0; i < n; i++)
            g.add(new ArrayList<>());
        for (int i = 0; i < m; i++) {
            int x = sc.nextInt() - 1;
            int y = sc.nextInt() - 1;
            int z = sc.nextInt();
            g.get(x).add(new Point(y, z));
            g.get(y).add(new Point(x, z));
            d.merge(x, y);
        }
        var fa = new ModIntFactory((int) 1e9 + 7);
        var P = fa.create(1);
        var Q = fa.create(1);
        var h = new long[2][n];
        Arrays.fill(h[0], u);
        Arrays.fill(h[1], u);
        var q = new ArrayDeque<Point2>();
        for (var G : d.groups()) {
            if (G.size() == 1) {
                P.mulAsg(k);
                Q.mulAsg(k - 1);
            } else {
                int R = G.get(0);
                h[0][R] = 0;
                q.add(new Point2(R, true));
                while (!q.isEmpty()) {
                    var r = q.removeFirst();
                    for (var i : g.get(r.x)) {
                        if (r.y) {
                            if (h[1][i.x] != u && h[1][i.x] != i.y - h[0][r.x])
                                P = Q = fa.create(0);
                            if (h[1][i.x] != i.y - h[0][r.x]) {
                                h[1][i.x] = i.y - h[0][r.x];
                                q.addLast(new Point2(i.x, !r.y));
                            }
                        } else {
                            if (h[0][i.x] != u && h[0][i.x] != i.y - h[1][r.x])
                                P = Q = fa.create(0);
                            if (h[0][i.x] != i.y - h[1][r.x]) {
                                h[0][i.x] = i.y - h[1][r.x];
                                q.addLast(new Point2(i.x, !r.y));
                            }
                        }
                    }
                }
                var no = false;
                for (int i = 0; i < n; i++)
                    no |= h[0][i] != u && h[1][i] != u;
                if (!no) {
                    long le = -u;
                    for (long i : h[0])
                        if (i != u)
                            le = max(le, i);
                    long ri = -u;
                    for (long i : h[1])
                        if (i != u)
                            ri = max(ri, i);
                    P.mulAsg(h(1 - longArray(h[0], Long::min), longArray(h[1], Long::min) - 1, ri - k, k - le));
                    Q.mulAsg(h(1 - longArray(h[0], Long::min), longArray(h[1], Long::min) - 1, ri - k + 1, k - 1 - le));
                } else {
                    for (int i = 0; i < n; i++) {
                        if ((h[0][i] - h[1][i]) % 2 != 0 || (h[0][i] + h[1][i]) <= 0)
                            P = Q = fa.create(0);
                        if ((h[0][i] + h[1][i]) > 2 * k)
                            P = fa.create(0);
                        if ((h[0][i] + h[1][i]) >= 2 * k)
                            Q = fa.create(0);
                    }
                }
            }
        }
        ou.println(P.sub(Q));
    }

    public static long h(long p, long q, long r, long s) {
        return p > q || r > s || q < r || s < p ? 0 : min(q, s) - max(p, r) + 1;
    }

    public static void main(String[] args) {
        var sc = new ContestScanner();
        var ou = new ContestPrinter();
        solve(sc, ou);
        ou.flush();
        ou.close();
    }

    public static int intArray(int[] a, java.util.function.IntBinaryOperator map) {
        int s = a[0];
        for (int i = 1; i < a.length; i++)
            s = map.applyAsInt(s, a[i]);
        return s;
    }

    public static long longArray(long[] a, java.util.function.LongBinaryOperator map) {
        long s = a[0];
        for (int i = 1; i < a.length; i++)
            s = map.applyAsLong(s, a[i]);
        return s;
    }

    public static int max(int s, int... a) {
        for (int i : a)
            if (s < i)
                s = i;
        return s;
    }

    public static long max(long s, long... a) {
        for (long i : a)
            if (s < i)
                s = i;
        return s;
    }

    public static int min(int s, int... a) {
        for (int i : a)
            if (s > i)
                s = i;
        return s;
    }

    public static long min(long s, long... a) {
        for (long i : a)
            if (s > i)
                s = i;
        return s;
    }
}

class Point {
    int x;
    int y;

    Point(int x, int y) {
        this.x = x;
        this.y = y;
    }

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

    @Override
    public int hashCode() {
        long result = x;
        result = 31 * result + y;
        return (int) result;
    }

    @Override
    public String toString() {
        return this.x + " " + this.y;
    }
}

class Point2 {
    int x;
    boolean y;

    Point2(int x, boolean y) {
        this.x = x;
        this.y = y;
    }

    @Override
    public boolean equals(Object o) {
        if (o == this)
            return true;
        if (o.getClass() != this.getClass())
            return false;
        Point2 p = (Point2) o;
        return this.x == p.x && this.y == p.y;
    }

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

    @Override
    public String toString() {
        return this.x + " " + this.y;
    }
}

class DSU {
    private int n;
    private int[] parentOrSize;

    public DSU(int n) {
        this.n = n;
        this.parentOrSize = new int[n];
        java.util.Arrays.fill(parentOrSize, -1);
    }

    int merge(int a, int b) {
        if (!(0 <= a && a < n))
            throw new IndexOutOfBoundsException("a=" + a);
        if (!(0 <= b && b < n))
            throw new IndexOutOfBoundsException("b=" + b);

        int x = leader(a);
        int y = leader(b);
        if (x == y)
            return x;
        if (-parentOrSize[x] < -parentOrSize[y]) {
            int tmp = x;
            x = y;
            y = tmp;
        }
        parentOrSize[x] += parentOrSize[y];
        parentOrSize[y] = x;
        return x;
    }

    boolean same(int a, int b) {
        if (!(0 <= a && a < n))
            throw new IndexOutOfBoundsException("a=" + a);
        if (!(0 <= b && b < n))
            throw new IndexOutOfBoundsException("b=" + b);
        return leader(a) == leader(b);
    }

    int leader(int a) {
        if (parentOrSize[a] < 0) {
            return a;
        } else {
            parentOrSize[a] = leader(parentOrSize[a]);
            return parentOrSize[a];
        }
    }

    int size(int a) {
        if (!(0 <= a && a < n))
            throw new IndexOutOfBoundsException("" + a);
        return -parentOrSize[leader(a)];
    }

    ArrayList<ArrayList<Integer>> groups() {
        int[] leaderBuf = new int[n];
        int[] groupSize = new int[n];
        for (int i = 0; i < n; i++) {
            leaderBuf[i] = leader(i);
            groupSize[leaderBuf[i]]++;
        }
        ArrayList<ArrayList<Integer>> result = new ArrayList<>(n);
        for (int i = 0; i < n; i++)
            result.add(new ArrayList<>(groupSize[i]));
        for (int i = 0; i < n; i++)
            result.get(leaderBuf[i]).add(i);
        result.removeIf(ArrayList::isEmpty);
        return result;
    }
}

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 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++) {
            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 (ma instanceof ModArithmetic.ModArithmeticMontgomery) {
                return ((ModArithmetic.ModArithmeticMontgomery) ma).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();
        }
        if (buflen <= 0)
            return false;
        return true;
    }

    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 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 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(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;
        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]);
        }
    }
}