Exam on Computer Graphics#5984
Professor Artur, who teaches computer graphics, is an enthusiast of the game of Nim and the Ben-Batzalel problem. During exams, he offers students a choice: either defeat him in Nim, or help solve the Ben-Batzalel problem. Knowing the problem is unsolvable, the students invariably choose to play Nim. However, aware that students have mastered the winning strategy through diligent study, the professor has decided to change the rules.
Suppose there are students in the class, numbered from to in the register. Each student takes the exam individually. Before each student enters the room, the professor arranges piles of cones on the floor, with A_i cones in the -th pile. If a student’s number in the register is , then during the game, both the student and Professor Artur may remove cones from at most different piles per turn (they may take different numbers of cones from each pile), but at least cone must be removed in each turn. The players take turns, starting with the student. The player who cannot make a move loses.
Your task is to determine which students have no chance of passing the exam, since the professor knows the winning strategy for this modified game and will use it optimally.
The first line contains a single integer (1 \leq n \leq 10000). The second line contains integers A_i (1 \leq A_i \leq 10^6), separated by spaces.
Output the student numbers, in increasing order, of those who cannot pass the exam, regardless of how they play. If all students can pass the exam, output .
Example 1