# Pair Sums to Power of Two

You are given a list of integers `nums`

. Return the number of pairs `i < j`

such that `nums[i] + nums[j]`

is equal to `2 ** k`

for some `0 ≤ k`

.

**Constraints**

`0 ≤ n ≤ 100,000`

where`n`

is the length of`nums`

https://binarysearch.com/problems/Pair-Sums-to-Power-of-Two

## Examples

### Example 1

**Input**

- nums =
`[1, 1, 3, 5]`

**Output**

- answer =
`4`

**Explanation**

We can have the following pairs that sums to power of `2`

`(1, 1)`

`(1, 3)`

`(1, 3)`

`(3, 5)`

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