2017-like Number

We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.

You are given Q queries.

In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.

Constraints

• 1≤Q≤10^5
• 1≤l_i≤r_i≤10^5
• l_i and r_i are odd.
• All input values are integers.

Input

Input is given from Standard Input in the following format:

Q l_1 r_1 : l_Q r_Q

Output

Print Q lines. The i-th line (1≤i≤Q) should contain the response to the i-th query.

Examples

Input

1 3 7

Output

2

Input

4 13 13 7 11 7 11 2017 2017

Output

1 0 0 1

Input

6 1 53 13 91 37 55 19 51 73 91 13 49

Output

4 4 1 1 1 2

inputFormat

input values are integers.

Input

Input is given from Standard Input in the following format:

Q l_1 r_1 : l_Q r_Q

outputFormat

Output

Print Q lines. The i-th line (1≤i≤Q) should contain the response to the i-th query.

Examples

Input

1 3 7

Output

2

Input

4 13 13 7 11 7 11 2017 2017

Output

1 0 0 1

Input

6 1 53 13 91 37 55 19 51 73 91 13 49

Output

4 4 1 1 1 2

样例

1
3 7

2