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.