How many natural numbers can be taken from 1 to 2009, so that the sum of any two numbers can not be divided by 14?

How many natural numbers can be taken from 1 to 2009, so that the sum of any two numbers can not be divided by 14?

The quotient of 2009 divided by 14 is 143 odd 7,1-2009 natural numbers divided by 14 are 1,2,3,4,. 13,0,1,2,3,4,. 13,0,1,2,3,. 13,0,1,2,3,. 13,0,1,2,3,4,5,6,7 respectively
That is to say, you can get data from these numbers
Let's see 0,1,2,3,4,..., 12,13. The combination of two numbers that can be divided into 14 is
0+0,1+13,2+12,3+11,4+10,5+9,6+8,7+7
First of all, if the remainder is 0 and 7, you can only take one (if you take two, you can add them and divide them by 14)
Secondly, when you take any other remainder, you can't take the corresponding divisible 14, for example, if you take 1, then 13 will be abandoned completely
And because the remainder of the last few numbers is 1, 2, 3, 4, 5, 6, it's better to take them from them. Then we can calculate the numbers that are eliminated. 142 residues are 0, 143 residues are 7, and 143 residues are (13, 12, 11, 10, 9, 8)
The total is 142 + 143 + 143 * 6 = 11432009 - 1143 = 866