Suppose there are $n$ lines $L_1, L_2, \ldots, L_n$ in the $xOy$ plane, none of which are perpendicular to the $x$-axis. If, when looking down from a height of positive infinity on the $y$-axis, at least one sub-segment of line $L_i$ is visible, then $L_i$ is said to be visible; otherwise, $L_i$ is said to be covered.

For example, given three lines: $L_1: y = -x$, $L_2: y = x$, and $L_3: y = 0$, then $L_1$ and $L_2$ are visible, while $L_3$ is covered.

Your task is: given $n$ lines $L_1, L_2, \ldots, L_n$, write a program to find all visible lines. For simplicity, assume all lines can be written in the form $Y=AX+B$, where $A$ and $B$ are integers with absolute values less than $500000$, and no two lines are identical.

Input

The first line contains an integer $n$, representing the number of lines. The next $n$ lines each contain two space-separated integers; the two integers on the $(i+1)$-th line correspond to $A_i$ and $B_i$ for line $L_i$. It is guaranteed that $-500000 < A_i, B_i < 500000$, $0 < n < 50000$, and no two lines are identical.

Output

Output a single line containing $m$ integers $t_1, t_2, \ldots, t_m$, representing that $L_{t_1}, L_{t_2}, \ldots, L_{t_m}$ are visible. Your program must ensure that the sequence $t_1, t_2, \ldots, t_m$ is in increasing order, with a single space between adjacent integers.

Examples

Input 1

3
-1 0
1 0
0 0

Output 1

1 2