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Problem Background

In a mysterious digital forest, Muxue the youth discovered a giant number triangle. Legend has it that a treasure is hidden at the bottom of the triangle, but it can only be obtained by finding a special path. The sum of the numbers along this path has a special requirement: its remainder modulo 7 must be minimal.

Problem Description

Muxue has a number triangle, where the i-th row contains i numbers. Starting from the top, one can move to one of the two adjacent numbers in the next row each time, until reaching the bottom.

Muxue wants to find a path such that the remainder of the sum of the numbers along the path modulo 7 is minimized. If multiple paths have the same remainder, choose the one with the largest sum.

Input Format

First line: An integer n (1 ≤ n ≤ 1000), representing the number of rows in the triangle.
Next n lines: The i-th line contains i integers, representing the numbers in the triangle (0 ≤ a_ij ≤ 10^9).

Output Format

Two integers, separated by a space: the minimal remainder and the corresponding maximum sum.

Sample Input and Output #1

Input #1

3
1
2 3
4 5 6

Output #1

0 10

Explanation/Notes

Explanation for Sample 1:
The path 1→2→5 has sum 8, remainder 1;
The path 1→3→6 has sum 10, remainder 3;
The path 1→2→4 has sum 7, remainder 0.
Therefore, the minimal remainder is 0, and the corresponding maximum sum is 10.

This problem uses Subtask bundled testing