Calling Tree Relay Order

A phone bank organizes emergency alerts through a calling tree: member 1 is the organizer and starts the relay, and every other member is reached by exactly one other member who calls them directly. When a member receives the alert, they call their own direct contacts one at a time, in a fixed order assigned to them in advance; before moving on to call their next direct contact, a member waits until that contact — and everyone that contact goes on to reach — has fully finished being notified. In other words, a member's contacts are always called out one full branch at a time, in their assigned order.

Given the calling tree, determine the exact order in which all n members receive the alert, starting with the organizer.

Input format

• Line 1: a single integer n, the number of members (numbered 1 to n; member 1 is the organizer).
• The next n-1 lines each contain two space-separated integers p c, meaning member p directly calls member c. Reading the n-1 lines from top to bottom gives, for every member, their direct contacts in the exact order that member calls them (lines sharing the same p keep the relative order of their c's as read).

Output format

Print the n member numbers in the order they receive the alert, space-separated on a single line, starting with 1.

Constraints

• 1 <= n <= 2000
• The n-1 edges form a valid tree rooted at member 1 (every member other than 1 has exactly one incoming edge, and member 1 has none).
• 1 <= p, c <= n, p != c.

4
1 2
1 3
2 4

1 2 4 3

4
1 2
1 3
1 4

1 2 3 4