Tak and Hotels

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

inputFormat

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

outputFormat

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

样例

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

4
2
1
2

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