{"raw_statement":[{"iden":"statement","content":"Alice and Bob play the following game. They choose a number N to play with. The rules are as follows:\n\n- They write each number from 1 to N on a paper and put all these papers in a jar.\n\n- Alice plays first, and the two players alternate.\n\n- In his/her turn, a player can select any available number M and remove its divisors including M.\n\n- The person who cannot make a move in his/her turn wins the game.\n\nAssuming both players play optimally, you are asked the following question: who wins the game?\n\nThe first line contains the number of test cases T (1  ≤  T  ≤  20). Each of the next T lines contains an integer (1  ≤  N  ≤  1,000,000,000).\n\nOutput T lines, one for each test case, containing Alice if Alice wins the game, or Bob otherwise.\n\n"},{"iden":"input","content":"The first line contains the number of test cases T (1  ≤  T  ≤  20). Each of the next T lines contains an integer (1  ≤  N  ≤  1,000,000,000)."},{"iden":"output","content":"Output T lines, one for each test case, containing Alice if Alice wins the game, or Bob otherwise."},{"iden":"examples","content":"Input251OutputAliceBob"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ M, N \\in \\mathbb{Z} $ denote the dimensions of the grid, with $ 5 \\leq M, N \\leq 1000 $.  \nLet $ Q \\in \\mathbb{Z} $ denote the number of moves, with $ 1 \\leq Q \\leq 10^5 $.  \nLet $ G \\in \\mathbb{Z}^{M \\times N} $ be the initial grid, where $ G_{i,j} $ is the value at row $ i $, column $ j $.  \nLet $ \\mathcal{M} = \\{ (y_1^{(k)}, x_1^{(k)}, y_2^{(k)}, x_2^{(k)}, A^{(k)}) \\mid k \\in \\{1, \\dots, Q\\} \\} $ be the set of moves, where for each move $ k $:  \n- $ (y_1^{(k)}, x_1^{(k)}) $ is the top-left corner,  \n- $ (y_2^{(k)}, x_2^{(k)}) $ is the bottom-right corner,  \n- $ A^{(k)} \\in \\mathbb{Z} $, $ |A^{(k)}| \\leq 100 $, is the value added to all cells in the rectangle.\n\n**Constraints**  \n1. $ 1 \\leq Q \\leq 10^5 $  \n2. $ 5 \\leq M, N \\leq 1000 $  \n3. For each move $ k $:  \n   - $ 1 \\leq y_1^{(k)} \\leq y_2^{(k)} \\leq M $  \n   - $ 1 \\leq x_1^{(k)} \\leq x_2^{(k)} \\leq N $  \n   - $ -100 \\leq A^{(k)} \\leq 100 $  \n4. For all $ i \\in \\{1, \\dots, M\\}, j \\in \\{1, \\dots, N\\} $: $ |G_{i,j}| \\leq 100 $\n\n**Objective**  \nCompute the final grid $ G' \\in \\mathbb{Z}^{M \\times N} $, where:  \n$$\nG'_{i,j} = G_{i,j} + \\sum_{\\substack{k=1 \\\\ (y_1^{(k)} \\leq i \\leq y_2^{(k)}) \\land (x_1^{(k)} \\leq j \\leq x_2^{(k)})}}^{Q} A^{(k)}\n$$  \nOutput $ G' $ as an $ M \\times N $ matrix.","simple_statement":"You are given an M×N grid with initial numbers. Then Q operations are given, each adding a value A to all cells in a rectangle from (Y1,X1) to (Y2,X2). Output the final grid after all operations.","has_page_source":false}