Popes

Source: UVa

Version: Phuoc Hung OJ Extended

Problem Statement

You are given the election years of the Popes in non-decreasing chronological order. Several elections may occur in the same year.

For a positive integer $Y$, a $Y$-year period starting in year $N$ contains the years from $N$ through $N+Y-1$.

Find a $Y$-year period containing the maximum number of elections. Print the maximum count, the election year of the first Pope in that period, and the election year of the last Pope in that period. If several periods have the same maximum count, choose the oldest one.

Input

The first line contains $Y$.

The second line contains $P$.

The next $P$ lines contain the election years in non-decreasing order.

Output

Print three integers: the maximum number of elections, the first election year, and the last election year.

Subtasks

• Subtask 1 — 20%: $P\le100$.
• Subtask 2 — 30%: $P\le5000$.
• Subtask 3 — 50%: $P\le100000$, the last year $L\le1000000$, and $Y\le L$.

Examples

Input

5
20
1
2
3
6
8
12
13
13
15
16
17
18
19
20
20
21
25
26
30
31

Output

6 16 20

Explanation

The five-year period from $16$ through $20$ contains six elections: $16,17,18,19,20,20$.