A remote sensor-relay network is organized as a binary tree of relay units rooted at a central hub. Every relay can forward its readings to up to two downstream relays: a primary link and a secondary link. During a routine firmware update, exactly one relay's secondary link — which should have been left empty — was mistakenly wired to a relay that already receives a feed from a different, shallower relay elsewhere in the network. This leaves one relay with two independent incoming feeds, and leaves exactly one relay faulty: its only outgoing link is this erroneous duplicate feed.

To restore the network, find that one faulty relay and decommission it — remove it, and every link originating from it, from the network — then report which relays remain.

It is guaranteed that:

• exactly one relay X, never the hub, has this problem; X's own primary link is empty (X has no legitimate downstream relay of its own);
• discarding only X's incoming link restores a single valid binary tree, rooted at the hub, spanning every one of the other relays.

Input format

• Line 1: a single integer n, the number of relay records.
• Next n lines: three integers v L R — the i-th relay's signal value v, and the 1-based indices (among these n records) of its primary (L) and secondary (R) downstream relays, or 0 if that link is absent. Relay 1 is always the central hub.

Output format

• Line 1: m, the number of relays remaining after decommissioning the faulty relay.
• Line 2: the signal values of the remaining relays, in a standard level-order traversal of the corrected network (top level to bottom level; within a level, in left-to-right order produced by visiting each relay's primary link before its secondary link), space-separated.

Constraints

• 3 <= n <= 2000
• 1 <= v <= 10^5, and all v are distinct.
• Exactly one relay X (X != 1) has a secondary link pointing at some relay Y that already has an incoming primary or secondary link from a different relay at a shallower depth than X; X's own primary link is 0. Every other link belongs to a single valid binary tree spanning all n relays, rooted at relay 1.

3
10 2 3
20 0 0
30 0 2

2
10 20

5
100 2 3
50 4 0
90 5 0
40 0 0
80 0 4

4
100 50 90 40