LogiQuest

459. Queue Reconstruction by Height

MediumGreedySorting

Each person is (h, k): height h, with exactly k people of height ≥ h in front. Reconstruct the queue and print one "h k" per line, front to back.

Input format

Line 1: n Next n lines: h k

Output format

The queue, one person per line.

Example 1

Input

6
7 0
4 4
7 1
5 0
6 1
5 2

Output

5 0
7 0
5 2
6 1
4 4
7 1

Example 2

Input

6
6 0
5 0
4 0
3 2
2 2
1 4

Output

4 0
5 0
2 2
3 2
1 4
6 0

Constraints

1 ≤ n ≤ 2000

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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