Statement

This is an interactive problem. Your program communicates with the evaluator: it should alternately write messages to the evaluator on the standard output and read the next input from the standard input. There is a hidden permutation P = [P_1, P_2, …, P_N] of the numbers 1, 2, …, N. You can ask questions in the form (i, j) with 1 ≤ i, j ≤ N. Note that i and j does not have to be distinct. The evaluator responds with the most significant bit of the bitwise AND of P_i and P_j. and y=13 = 1101_(2), then their bitwise AND will be 9 = 1001_(2). Here, the most significant bit of a number x is the exponent of the highest power of 2 that appears when writing x in base 2. For example, the most significant bit of 5 = 101_(2) is 2, since 2^2 appears in the binary representation of 5. If the bitwise AND of P_i and P_j is 0, the evaluator responds with -1. Your task is to determine the hidden permutation of at most 1000 numbers by asking no more than \constraints30000 questions.