LogiQuest

395. Level Sums and Widest Level

MediumBFS

Print the sum of each level on one line, then on the next line print the 1-based level with the maximum sum (the smallest such level if tied).

Input format

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

Output format

Line 1: level sums Line 2: best level

Example 1

Input

7
1 7 0 7 -8 -1 -1

Output

1 7 -1
2

Example 2

Input

9
989 -1 10250 98693 -89388 -1 -1 -1 -32127

Output

989 10250 9305 -32127
2

Constraints

1 ≤ nodes ≤ 10⁴

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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