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 LuaJIT (2.0.4) (judge verdict: Accepted)

local function reada(n,m)m=m or 1 r={}for i=1,m do r[i]={}end for i=1,n do for j=1,m do r[j][i]=io.read"*n"end end return unpack(r)end
local function b_search(t,k,min,max)
	if(min>max)then return -1 end
	local mid=min+math.floor((max-min)/2)
	if(t[mid]>k)then return b_search(t,k,min,mid-1)
	elseif(t[mid]<k)then return b_search(t,k,mid+1,max)
	else return mid
	end
end

Q=io.read"*n"
l,r=reada(Q,2)

a={2}
for i=3,200000,2 do
	table.insert(a,i)
end

for i=3,math.sqrt(200000),2 do
	local b={}
	for _,v in ipairs(a)do
		if(v%i~=0 or v==i)then table.insert(b,v)end
	end
	a=b
end

s={0}
for i=1,50000 do
	if(b_search(a,i,1,#a)~=-1 and b_search(a,i*2-1,1,#a)~=-1)then
		s[i+1]=s[i]+1
	else
		s[i+1]=s[i]
	end
end

for i=1,Q do
	print(s[(r[i]+1)/2+1]-s[(l[i]+1)/2])
end