N hotels are located on a straight line. The coordinate of the i-th hotel (1 \leq i \leq N) is x_i.

Tak the traveler has the following two personal principles:

* He never travels a distance of more than L in a single day.
* He never sleeps in the open. That is, he must stay at a hotel at the end of a day.



You are given Q queries. The j-th (1 \leq j \leq Q) query is described by two distinct integers a_j and b_j. For each query, find the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel following his principles. It is guaranteed that he can always travel from the a_j-th hotel to the b_j-th hotel, in any given input.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq L \leq 10^9
* 1 \leq Q \leq 10^5
* 1 \leq x_i < x_2 < ... < x_N \leq 10^9
* x_{i+1} - x_i \leq L
* 1 \leq a_j,b_j \leq N
* a_j \neq b_j
* N,\,L,\,Q,\,x_i,\,a_j,\,b_j are integers.

Input

The input is given from Standard Input in the following format:


N
x_1 x_2 ... x_N
L
Q
a_1 b_1
a_2 b_2
:
a_Q b_Q


Output

Print Q lines. The j-th line (1 \leq j \leq Q) should contain the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel.

Example

Input

9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5


Output

4
2
1
2
import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;


public class Main {
    public static void main(String[] args) {
        FastScanner fsc = new FastScanner();
        int n = fsc.nextInt();
        long[] x = new long[n];
        for (int i = 0; i < n; i++) {
            x[i] = fsc.nextLong();
        }
        long l = fsc.nextLong();
        int p = minimumPowerOfTwo(n);
        int[][] right = new int[n][p];
        int u = 0, v = 0;
        while (u < n) {
            while (v < n && x[v] - x[u] <= l) {
                v++;
            }
            right[u][0] = v - 1;
            u++;
        }
        for (int k = 1; k < p; k++) {
            for (int i = 0; i < n; i++) {
                right[i][k] = right[right[i][k - 1]][k - 1];
            }
        }
        StringBuilder sb = new StringBuilder();
        int q = fsc.nextInt();
        for (int i = 0; i < q; i++) {
            int a = fsc.nextInt() - 1;
            int b = fsc.nextInt() - 1;
            if (a > b) {
                int tmp = a;
                a = b;
                b = tmp;
            }
            int day = 0;
            int now = a;
            while (now < b) {
                int fail = -1, pass = p;
                while (pass - fail > 1) {
                    int mid = fail + (pass - fail) / 2;
                    if (right[now][mid] >= b) {
                        pass = mid;
                    } else {
                        fail = mid;
                    }
                }
                if (fail == -1) {
                    day++;
                    break;
                }
                day += 1 << fail;
                now = right[now][fail];
            }
            sb.append(day).append('\n');
        }
        System.out.print(sb);
    }

    private static int minimumPowerOfTwo(int n) {
        int i = 0;
        while (1 << ++i < n)
            ;
        return i;
    }
}


class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -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 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());}
}
