A sequence $$$a_1, a_2, \dots, a_n$$$ is called good if, for each element $$$a_i$$$, there exists an element $$$a_j$$$ ($$$i \ne j$$$) such that $$$a_i+a_j$$$ is a power of two (that is, $$$2^d$$$ for some non-negative integer $$$d$$$).

For example, the following sequences are good:

• $$$[5, 3, 11]$$$ (for example, for $$$a_1=5$$$ we can choose $$$a_2=3$$$. Note that their sum is a power of two. Similarly, such an element can be found for $$$a_2$$$ and $$$a_3$$$),
• $$$[1, 1, 1, 1023]$$$,
• $$$[7, 39, 89, 25, 89]$$$,
• $$$[]$$$.

Note that, by definition, an empty sequence (with a length of $$$0$$$) is good.

For example, the following sequences are not good:

• $$$[16]$$$ (for $$$a_1=16$$$, it is impossible to find another element $$$a_j$$$ such that their sum is a power of two),
• $$$[4, 16]$$$ (for $$$a_1=4$$$, it is impossible to find another element $$$a_j$$$ such that their sum is a power of two),
• $$$[1, 3, 2, 8, 8, 8]$$$ (for $$$a_3=2$$$, it is impossible to find another element $$$a_j$$$ such that their sum is a power of two).

You are given a sequence $$$a_1, a_2, \dots, a_n$$$. What is the minimum number of elements you need to remove to make it good? You can delete an arbitrary set of elements.