2023: [USACO 2024 February Contest Bronze] Problem 1. Palindrome Game

Bessie and Elsie are playing a game with a pile of stones that initially contains $S$ stones ($1\le S<{10}^{{10}^5}$). The two cows alternate turns, with Bessie going first. When it is a cow's turn, she must remove $x$ stones from the pile, where $x$ is any positive integer palindrome of the cow's choosing. If the pile is empty when a cow's turn starts, that cow loses.

Definition: A positive integer is a palindrome if it reads the same forward and backward; examples of palindromes include 1, 121, and 9009. Leading zeros are not allowed; e.g., 990 is *not* a palindrome.

There are $T$ ($1\le T\le 10$) independent test cases. For each test case, print who wins the game if both cows play optimally.

Each test case is specified by a single integer $S$.

3
8
10
12

B
E
B