LogiQuest

381. Minimum Depth

EasyBFS

Print the number of nodes on the shortest path from the root to a leaf (a node with no children).

Input format

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

Output format

The minimum depth.

Example 1

Input

7
3 9 20 -1 -1 15 7

Output

2

Example 2

Input

9
2 -1 3 -1 4 -1 5 -1 6

Output

5

Constraints

1 ≤ nodes ≤ 10⁴

Read input from standard input and print the answer to standard output. Your code is judged against 3 test cases, most of them hidden.

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