Odd vs. Even Showdown

Among the natural numbers from 1 to $n$, are there more even numbers or more odd numbers?

The first line gives the number of test cases $T$ ($0 \le T \le 1\,000\,000$). Each test case consists of a single line containing a natural number $n$ with $1 \le n \le 10^9$.

For each test case, print O on its own line if the even numbers are not fewer than the odd numbers, and E otherwise.

Yes, that must surely be correct...

The problem is so easy that, to make it at least a little trashy, the samples have been hidden.

Contest > Gudeogi Cup > True Final Gudeogi Cup 2 Problem 🆚

• Problem author: jh05013

• The samples are not scored.

Unlike the usual definitions, this problem defines odd and even as follows.

Every natural number $k \ge 1$ can be written as a product of primes, and that representation is unique up to the order of the primes. If the number of primes used is not a multiple of 2, then $k$ is even; otherwise $k$ is odd. (When $k = 1$, it is the product of 0 primes, and 0 is a multiple of 2.) If the same prime is used several times, each use must be counted separately.