LogiQuest

385. Height-Balanced Tree

EasyDFS

Print YES if, for every node, the heights of its two subtrees differ by at most one, else NO.

Input format

Line 1: n (number of level-order entries) Line 2: the values in level order, -1 for a missing child

Output format

YES or NO

Example 1

Input

7
3 9 20 -1 -1 15 7

Output

YES

Example 2

Input

9
1 2 2 3 3 -1 -1 4 4

Output

NO

Constraints

1 ≤ nodes ≤ 5000

Read input from standard input and print the answer to standard output. Your code is judged against 5 test cases, most of them hidden.

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