Piles Parity Codechef Solution

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Piles Parity Codechef Solution

Piles Parity Codechef Solution

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Problem

Chef and Chefina are playing a game involving N piles where the i^{th} pile (1\le i \le N) has A_i stones initially.

They take alternate turns with Chef starting the game.

In his/her turn a player can choose any non-empty pile (say i^{th} pile) and remove X stones from it iff:

  • Parity of X is same as parity of i.
  • 1 \leq X \leq A_i.

The player who cannot make a move loses. Determine the winner of the game if both players play optimally.

Input Format

  • The first line of input will contain a single integer T, denoting the number of test cases.
  • Each test case consists of multiple lines of input.
    • The first line of each test case contains a single integer N — the number of piles.
    • Next line contains N space-separated integers A_1, A_2, A_3, \dots, A_N – denoting the number of stones in each pile initially.

Output Format

For each test case, output CHEF if Chef wins the game, CHEFINA otherwise.

The output is case-insensitive. Thus, the strings ChefCHEFchef, and cheF are all considered identical.

Constraints

  • 1 \leq T \leq 4000
  • 1 \leq N \leq 10^5
  • 1 \leq A_i \leq 10^9
  • Sum of N over all test cases does not exceed 2 \cdot 10^5

Sample 1:

Input

Output

2
1
2
3
2 1 3
CHEFINA
CHEF

Explanation:

Test case 1: Chef makes the first move and can only remove X = 1 stone from the pile. Thus, the pile has 1 stone left which Chefina can remove. Chef has no possible move left and thus Chefina wins.
Note that Chef cannot remove X = 2 stones in the first turn as X should have the same parity as i = 1.

Test case 2: It can be shown that if both players play optimally, Chef wins the game.

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SOLUTION

Piles Parity Codechef Solution

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