Manao is solving a problem with the following statement:

<image>

He came up with a solution that produces the correct answers but is too slow. You are given the pseudocode of his solution, where the function getAnswer calculates the answer to the problem:
    
    
      
    getAnswer(a[1..n], b[1..len], h)  
      answer = 0  
      for i = 1 to n-len+1  
        answer = answer + f(a[i..i+len-1], b, h, 1)  
      return answer  
      
    f(s[1..len], b[1..len], h, index)  
      if index = len+1 then  
        return 1  
      for i = 1 to len  
        if s[index] + b[i] >= h  
          mem = b[i]  
          b[i] = 0  
          res = f(s, b, h, index + 1)  
          b[i] = mem  
          if res > 0  
            return 1  
      return 0  
    

Your task is to help Manao optimize his algorithm.

Input

The first line contains space-separated integers n, len and h (1 ≤ len ≤ n ≤ 150000; 1 ≤ h ≤ 109). The second line contains len space-separated integers b1, b2, ..., blen (1 ≤ bi ≤ 109). The third line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print a single number — the answer to Manao's problem.

Examples

Input

5 2 10
5 3
1 8 5 5 7


Output

2
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.stream.IntStream;
import java.util.Arrays;
import java.util.Random;
import java.util.function.Supplier;
import java.io.OutputStreamWriter;
import java.util.function.IntFunction;
import java.io.OutputStream;
import java.io.PrintStream;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.util.function.Consumer;
import java.io.Closeable;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            EOptimize solver = new EOptimize();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class EOptimize {
        Debug debug = new Debug(true);

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.ri();
            int m = in.ri();
            int h = in.ri();
            int[] b = in.ri(m);
            Arrays.sort(b);
            int[] a = in.ri(n);
            int[] indices = IntStream.range(0, n).toArray();
            int[] rank = new int[n];
            SortUtils.quickSort(indices, (i, j) -> Integer.compare(a[i], a[j]), 0, n);
            for (int i = 0; i < n; i++) {
                rank[indices[i]] = i;
            }
            SegTree<SumImpl, UpdateImpl> st = new SegTree<>(0, n - 1, SumImpl::new, UpdateImpl::new,
                    i -> {
                        SumImpl ans = new SumImpl();
                        return ans;
                    });
            SumImpl sum = new SumImpl();
            UpdateImpl upd = new UpdateImpl();
            int ans = 0;
            for (int i = 0; i < n; i++) {
                sum.clear();
                st.query(0, rank[i], 0, n - 1, sum);
                int size = sum.size;
                int match = BinarySearch.lowerBound(b, 0, m - 1, h - a[i]);
                upd.clear();
                upd.isSet = true;
                upd.set = size + match;
                upd.size = 1;
                st.update(rank[i], rank[i], 0, n - 1, upd);
                upd.clear();
                upd.set = 1;
                st.update(rank[i] + 1, n - 1, 0, n - 1, upd);
                debug.debug("i", i);
                debug.debug("st", st);
                if (i >= m - 1) {
                    if (st.sum.max < m) {
                        ans++;
                    }
                    int remove = rank[i - (m - 1)];
                    upd.clear();
                    upd.set = 0;
                    upd.size = -1;
                    upd.isSet = true;
                    st.update(remove, remove, 0, n - 1, upd);
                    upd.clear();
                    upd.set = -1;
                    st.update(remove + 1, n - 1, 0, n - 1, upd);
                }
            }

            out.println(ans);
        }

    }

    static class UpdateImpl extends CloneSupportObject<UpdateImpl> implements Update<UpdateImpl> {
        int set;
        boolean isSet;
        int size;

        public void update(UpdateImpl update) {
            if (update.isSet) {
                set = update.set;
                isSet = true;
            } else {
                set += update.set;
            }
            size += update.size;
        }

        public void clear() {
            set = 0;
            isSet = false;
            size = 0;
        }

        public boolean ofBoolean() {
            return !(set == 0 && isSet == false && size == 0);
        }

    }

    static interface Update<U extends Update<U>> extends Cloneable {
        void update(U u);

        void clear();

        boolean ofBoolean();

        U clone();

    }

    static class SegTree<S extends Sum<S, U>, U extends Update<U>> implements Cloneable {
        private SegTree<S, U> left;
        private SegTree<S, U> right;
        public S sum;
        private U update;

        private void modify(U x) {
            update.update(x);
            sum.update(x);
        }

        private void pushDown() {
            if (update.ofBoolean()) {
                left.modify(update);
                right.modify(update);
                update.clear();
                assert !update.ofBoolean();
            }
        }

        private void pushUp() {
            sum.copy(left.sum);
            sum.add(right.sum);
        }

        public SegTree(int l, int r, Supplier<S> sSupplier, Supplier<U> uSupplier,
                       IntFunction<S> func) {
            update = uSupplier.get();
            update.clear();
            if (l < r) {
                sum = sSupplier.get();
                int m = DigitUtils.floorAverage(l, r);
                left = new SegTree<>(l, m, sSupplier, uSupplier, func);
                right = new SegTree<>(m + 1, r, sSupplier, uSupplier, func);
                pushUp();
            } else {
                sum = func.apply(l);
            }
        }

        private boolean cover(int L, int R, int l, int r) {
            return L <= l && R >= r;
        }

        private boolean leave(int L, int R, int l, int r) {
            return R < l || L > r;
        }

        public void update(int L, int R, int l, int r, U u) {
            if (leave(L, R, l, r)) {
                return;
            }
            if (cover(L, R, l, r)) {
                modify(u);
                return;
            }
            int m = DigitUtils.floorAverage(l, r);
            pushDown();
            left.update(L, R, l, m, u);
            right.update(L, R, m + 1, r, u);
            pushUp();
        }

        public void query(int L, int R, int l, int r, S s) {
            if (leave(L, R, l, r)) {
                return;
            }
            if (cover(L, R, l, r)) {
                s.add(sum);
                return;
            }
            int m = DigitUtils.floorAverage(l, r);
            pushDown();
            left.query(L, R, l, m, s);
            right.query(L, R, m + 1, r, s);
        }

        public SegTree<S, U> deepClone() {
            SegTree<S, U> clone = clone();
            clone.sum = clone.sum.clone();
            clone.update = clone.update.clone();
            if (clone.left != null) {
                clone.left = clone.left.deepClone();
                clone.right = clone.right.deepClone();
            }
            return clone;
        }

        public void visitLeave(Consumer<SegTree<S, U>> consumer) {
            if (left == null) {
                consumer.accept(this);
                return;
            }
            pushDown();
            left.visitLeave(consumer);
            right.visitLeave(consumer);
        }

        public String toString() {
            StringBuilder ans = new StringBuilder();
            deepClone().visitLeave(x -> ans.append(x.sum).append(' '));
            return ans.toString();
        }

        public SegTree<S, U> clone() {
            try {
                return (SegTree<S, U>) super.clone();
            } catch (CloneNotSupportedException e) {
                throw new UnsupportedOperationException(e);
            }
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        public void populate(int[] data) {
            for (int i = 0; i < data.length; i++) {
                data[i] = readInt();
            }
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int ri() {
            return readInt();
        }

        public int[] ri(int n) {
            int[] ans = new int[n];
            populate(ans);
            return ans;
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class DigitUtils {
        private DigitUtils() {
        }

        public static int floorAverage(int x, int y) {
            return (x & y) + ((x ^ y) >> 1);
        }

    }

    static interface Sum<S, U> extends Cloneable {
        void add(S s);

        void update(U u);

        void copy(S s);

        S clone();

    }

    static class SumImpl implements Sum<SumImpl, UpdateImpl> {
        int max;
        int size;

        void clear() {
            max = 0;
            size = 0;
        }

        public void add(SumImpl sum) {
            max = Math.max(max, sum.max);
            size += sum.size;
        }

        public void update(UpdateImpl update) {
            size += update.size;
            if (size == 0) {
                max = 0;
                return;
            }
            if (update.isSet) {
                max = update.set;
            } else {
                max += update.set;
            }
        }

        public void copy(SumImpl sum) {
            this.max = sum.max;
            this.size = sum.size;
        }

        public SumImpl clone() {
            SumImpl ans = new SumImpl();
            ans.copy(this);
            return ans;
        }

        public String toString() {
            return String.format("(%d, %d)", max, size);
        }

    }

    static class RandomWrapper {
        private Random random;
        public static final RandomWrapper INSTANCE = new RandomWrapper();

        public RandomWrapper() {
            this(new Random());
        }

        public RandomWrapper(Random random) {
            this.random = random;
        }

        public RandomWrapper(long seed) {
            this(new Random(seed));
        }

        public int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }

    }

    static class SequenceUtils {
        public static void swap(int[] data, int i, int j) {
            int tmp = data[i];
            data[i] = data[j];
            data[j] = tmp;
        }

    }

    static abstract class CloneSupportObject<T> implements Cloneable {
        public T clone() {
            try {
                return (T) super.clone();
            } catch (CloneNotSupportedException e) {
                throw new RuntimeException(e);
            }
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 32 << 10;
        private final Writer os;
        private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length() < THRESHOLD) {
                return;
            }
            flush();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput println(int c) {
            return append(c).println();
        }

        public FastOutput println() {
            return append('\n');
        }

        public FastOutput flush() {
            try {
//            boolean success = false;
//            if (stringBuilderValueField != null) {
//                try {
//                    char[] value = (char[]) stringBuilderValueField.get(cache);
//                    os.write(value, 0, cache.length());
//                    success = true;
//                } catch (Exception e) {
//                }
//            }
//            if (!success) {
                os.append(cache);
//            }
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class SortUtils {
        private static final int THRESHOLD = 8;

        private SortUtils() {
        }

        public static void insertSort(int[] data, IntegerComparator cmp, int l, int r) {
            for (int i = l + 1; i <= r; i++) {
                int j = i;
                int val = data[i];
                while (j > l && cmp.compare(data[j - 1], val) > 0) {
                    data[j] = data[j - 1];
                    j--;
                }
                data[j] = val;
            }
        }

        public static void quickSort(int[] data, IntegerComparator cmp, int f, int t) {
            if (t - f <= THRESHOLD) {
                insertSort(data, cmp, f, t - 1);
                return;
            }
            SequenceUtils.swap(data, f, RandomWrapper.INSTANCE.nextInt(f, t - 1));
            int l = f;
            int r = t;
            int m = l + 1;
            while (m < r) {
                int c = cmp.compare(data[m], data[l]);
                if (c == 0) {
                    m++;
                } else if (c < 0) {
                    SequenceUtils.swap(data, l, m);
                    l++;
                    m++;
                } else {
                    SequenceUtils.swap(data, m, --r);
                }
            }
            quickSort(data, cmp, f, l);
            quickSort(data, cmp, m, t);
        }

    }

    static class Debug {
        private boolean offline;
        private PrintStream out = System.err;
        static int[] empty = new int[0];

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager() == null;
        }

        public Debug debug(String name, int x) {
            if (offline) {
                debug(name, "" + x);
            }
            return this;
        }

        public Debug debug(String name, String x) {
            if (offline) {
                out.printf("%s=%s", name, x);
                out.println();
            }
            return this;
        }

        public Debug debug(String name, Object x) {
            return debug(name, x, empty);
        }

        public Debug debug(String name, Object x, int... indexes) {
            if (offline) {
                if (x == null || !x.getClass().isArray()) {
                    out.append(name);
                    for (int i : indexes) {
                        out.printf("[%d]", i);
                    }
                    out.append("=").append("" + x);
                    out.println();
                } else {
                    indexes = Arrays.copyOf(indexes, indexes.length + 1);
                    if (x instanceof byte[]) {
                        byte[] arr = (byte[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof short[]) {
                        short[] arr = (short[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof boolean[]) {
                        boolean[] arr = (boolean[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof char[]) {
                        char[] arr = (char[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof int[]) {
                        int[] arr = (int[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof float[]) {
                        float[] arr = (float[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof double[]) {
                        double[] arr = (double[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof long[]) {
                        long[] arr = (long[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else {
                        Object[] arr = (Object[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    }
                }
            }
            return this;
        }

    }

    static class BinarySearch {
        private BinarySearch() {
        }

        public static int lowerBound(int[] arr, int l, int r, int target) {
            while (l < r) {
                int mid = DigitUtils.floorAverage(l, r);
                if (arr[mid] >= target) {
                    r = mid;
                } else {
                    l = mid + 1;
                }
            }
            if (arr[l] < target) {
                l++;
            }
            return l;
        }

    }

    static interface IntegerComparator {
        public int compare(int a, int b);

    }
}

