Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

1
3 7

Sample Output 1

2

3 is similar to 2017, since both 3 and (3+1)/2=2 are prime.

5 is similar to 2017, since both 5 and (5+1)/2=3 are prime.

7 is not similar to 2017, since (7+1)/2=4 is not prime, although 7 is prime.

Thus, the response to the first query should be 2.

Sample Input 2

4
13 13
7 11
7 11
2017 2017

Sample Output 2

1
0
0
1

Note that 2017 is also similar to 2017.

Sample Input 3

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

Sample Output 3

4
4
1
1
1
2

Solution in Ruby (2.3.3) (judge verdict: Accepted)

q = gets.to_i
lr = []
q.times do
  lr.push gets.split.map(&:to_i)
end
s = [3,5,13,37,61,73,157,193,277,313,397,421,457,541,613,661,673,733,757,877,997,1093,1153,1201,1213,1237,1321,1381,1453,1621,1657,1753,1873,1933,1993,2017,2137,2341,2473,2557,2593,2797,2857,2917,3061,3217,3253,3313,3517,3733,4021,4057,4177,4261,4273,4357,4441,4561,4621,4933,5077,5101,5113,5233,5413,5437,5581,5701,6037,6073,6121,6133,6217,6337,6361,6373,6637,6661,6781,6997,7057,7213,7393,7417,7477,7537,7753,7933,8053,8101,8221,8317,8353,8461,8521,8677,8713,8893,9013,9133,9181,9241,9277,9601,9661,9721,9817,9901,9973,10333,10357,10453,10837,10861,10957,11113,11161,11317,11497,11677,11701,12073,12157,12241,12301,12421,12433,12457,12541,12553,12601,12721,12757,12841,12853,13093,13381,13417,13681,13921,13933,14437,14593,14737,14821,15013,15073,15121,15241,15277,15361,15373,15733,15901,16033,16333,16381,16417,16573,16633,16657,16921,17041,17053,17077,17257,17293,17377,17881,18013,18097,18133,18181,18217,18253,18301,18313,18397,18481,18553,18637,18793,19237,19441,19477,19717,19801,19813,19861,20353,20533,20641,20857,21001,21061,21193,21277,21313,21577,21661,21673,21817,22093,22501,22573,22621,22993,23053,23173,23557,23677,23773,23917,24097,24421,24481,24781,24841,25033,25153,25237,25561,25657,25933,26017,26293,26317,26437,26497,26821,26833,26881,26953,27073,27253,27337,27361,27457,27997,28057,28297,28393,28813,28837,28921,29101,29473,29641,30181,30241,30517,30553,30577,30637,30661,30697,30781,30853,31081,31237,31321,31333,31357,31477,31573,31873,31981,32173,32377,32497,32533,32833,33037,33301,33457,33493,33757,33961,34057,34213,34273,34381,34513,34897,34981,35317,35521,35677,35977,36097,36241,36433,36457,36793,36877,36901,36913,37273,37321,37357,37573,37717,37957,38281,38461,38833,38953,38977,39217,39373,39397,39733,40093,40177,40213,40693,40813,41017,41221,41281,41413,41617,41893,42061,42337,42373,42793,42961,43117,43177,43201,43321,43573,43597,43633,43717,44053,44101,44221,44257,44293,44893,45061,45337,45433,45481,45553,45613,45841,46021,46141,46261,46861,46993,47017,47161,47353,47521,47533,47653,47713,47737,47797,47857,48121,48193,48337,48673,48757,48781,49033,49261,49393,49417,49597,49681,49957,50221,50341,50377,50821,50893,51157,51217,51241,51481,51517,51637,52057,52081,52237,52321,52453,52501,52813,52861,52957,53077,53113,53281,53401,53917,54121,54133,54181,54217,54421,54517,54541,54673,54721,54973,55057,55381,55501,55633,55837,55921,55933,56053,56101,56113,56197,56401,56437,56701,56773,56821,56857,56893,57073,57097,57193,57241,57373,57457,57853,58153,58417,58441,58537,58573,58693,59053,59197,59221,59281,59341,59833,60217,60337,60373,60637,60733,60937,61057,61153,61261,61297,61561,61657,61681,61717,61861,62137,62473,62497,62533,62653,62773,63313,63397,63541,63697,63781,63913,64153,64237,64381,64513,64717,65173,65293,65413,65437,65497,65557,65677,65881,66301,66361,66601,66697,66853,66973,67057,67153,67273,67477,67537,67741,67777,67933,67993,68113,68281,68521,68737,69001,69073,69457,69493,69697,69877,70117,70177,70297,70501,70621,70921,70981,71233,71341,71353,71593,71821,72073,72481,72613,72901,72937,73141,73417,73477,73561,73693,74077,74317,74377,74713,75013,75133,75181,75721,75793,75913,76333,76561,76597,76753,77137,77641,78157,78193,78277,78877,78901,79333,79357,79537,79657,79693,79801,79873,80077,80173,80221,80473,80701,80713,80917,81013,81181,81517,81637,81853,82021,82153,82261,82561,82981,83077,83221,83233,83437,83617,83701,83773,84121,84313,84673,84697,84793,84913,85297,85333,85453,85717,85933,86353,86413,87181,87253,87337,87421,87433,87517,87553,87973,88117,88177,88237,88261,88513,88741,88897,88993,89293,89833,89917,90121,91081,91381,91393,91513,91957,92041,92557,92761,92821,92893,92941,93097,93133,93493,93637,93913,94033,94117,94273,94321,94441,94573,94777,94837,94993,95257,95317,95401,95581,95617,95713,95737,96097,96157,96181,96493,96517,96973,97081,97177,97501,97561,97777,97813,98017,98737,98953,99277,99577,99661,99877]
lr.each do |e|
  l = e.first
  r = e.last
  li = s.bsearch_index { |x| l < x }
  ri = s.bsearch_index { |x| r < x }
  li = s.size unless li
  ri = s.size unless ri
  if li > 0 && s[li - 1] >= l
    li -= 1
  end
  if ri > 0 && s[ri - 1] <= r
    ri -= 1
  end
  puts ri - li + 1
end