Uniform Frequency Relay Network

A relay operator manages a hierarchical broadcast network of n towers arranged as a rooted binary tree: tower 0 is the network's hub, and every other tower is reached from the hub by following a chain of left/right relay links. Each tower continuously transmits on one integer frequency. The operator wants to know whether the entire network is broadcasting on a single uniform frequency, i.e. whether every tower's frequency equals the hub's frequency.

Input format

• Line 1: a single integer n — the number of towers (1 <= n <= 100).
• Each of the next n lines describes tower i (0-indexed, i from 0 to n-1) as three integers val_i left_i right_i, where val_i (0 <= val_i <= 99) is tower i's frequency, and left_i and right_i are the indices of tower i's left and right child towers, or -1 if that side has no child. Tower 0 is the hub, and the described structure always forms a valid rooted binary tree containing all n towers.

Output format

Print true if every tower's frequency equals the hub's frequency, or false otherwise.

Constraints

• 1 <= n <= 100
• 0 <= val_i <= 99
• Every index other than -1 that appears as a left_i or right_i is a valid tower index in [0, n-1], each tower is the child of at most one other tower, and the whole structure is a valid rooted binary tree rooted at tower 0 (every tower is reachable from tower 0).

4
5 1 2
5 3 -1
5 -1 -1
5 -1 -1

true

3
5 1 2
5 -1 -1
7 -1 -1

false