Assembly Line Component Finish Order

A factory builds one master assembly out of sub-components, and each of those sub-components may itself be built from smaller sub-components, and so on. For every component, its direct sub-components must be attached in a fixed left-to-right order, and a component cannot be marked finished until every one of its direct sub-components has already been finished (finishing a sub-component means its own entire sub-tree of parts is already complete). Given the full parts breakdown, output the order in which all components, including the master assembly itself, get marked finished.

Input format

Line 1: an integer N — the number of components, numbered 1..N, where component 1 is the master assembly (the root). Next N lines, one for each component from 1 to N in order: a line for component i begins with an integer k_i — the number of direct sub-components of component i — followed by k_i integers, the ids of those sub-components listed in the exact order they are attached (left to right). If k_i = 0 there are no further integers on that line.

Output format

Print a single line with the ids of all N components, space-separated, in the order they are finished.

Constraints

1 <= N <= 10^5 0 <= k_i <= N-1 The sum of all k_i equals N-1. Every component id other than 1 appears as a direct sub-component of exactly one component, and together with the root this always forms a valid tree.

4
2 2 3
1 4
0
0

4 2 3 1

1
0

1