Jumps

"Jumps" is a board game played on a tape of squares that extends without bound to the left and to the right. Finitely many pieces stand on the squares, and a single square may hold more than one piece. The leftmost non-empty square is numbered 0. Squares to the right are numbered 1, 2, 3, ..., and squares to the left are numbered -1, -2, -3, .... A configuration is described by listing, for every occupied square, the square's number together with the number of pieces on it.

Two kinds of moves change a configuration:

• Jump right: remove one piece from a square $p$ and one piece from square $p+1$, then place one piece on square $p+2$.
• Jump left: remove one piece from a square $p+2$, then place one piece on square $p+1$ and one piece on square $p$.

A configuration is final when every pair of neighbouring squares holds at most one piece in total. Starting from any configuration, a finite sequence of moves always leads to exactly one final configuration.

Given the initial configuration, compute the final configuration it reaches.

The first line contains one integer $n$ ($1 \le n \le 10000$), the number of non-empty squares in the initial configuration.

Each of the next $n$ lines describes one non-empty square with two integers: the square's number and the number of pieces on it. The squares are listed in increasing order of their numbers. Every square number is at most $10000$, and every square holds at most $10^8$ pieces.

Print a single line with the numbers of the occupied squares of the final configuration, in increasing order, separated by single spaces.