Problem3057--Pair of Numbers

3057: Pair of Numbers

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Simon has an array a1,a2,...,an, consisting of n positive integers. Today Simon asked you to find a pair of integers l,r (1≤l≤r≤n), such that the following conditions hold:

  1. there is integer j (l≤j≤r), such that all integers al,al+1,...,ar are divisible by aj;
  2. value r-l takes the maximum value among all pairs for which condition 1 is true;

Help Simon, find the required pair of numbers (l,r). If there are multiple required pairs find all of them.

Input

The first line contains integer n (1≤n≤3·105).

The second line contains n space-separated integers a1,a2,...,an (1≤ai≤106).

Output

Print two integers in the first line − the number of required pairs and the maximum value of r-l. On the following line print all l values from optimal pairs in increasing order.

Examples
Input
5
4 6 9 3 6
Output
1 3
2
Input
5
1 3 5 7 9
Output
1 4
1
Input
5
2 3 5 7 11
Output
5 0
1 2 3 4 5
Note

In the first sample the pair of numbers is right, as numbers 6,9,3 are divisible by 3.

In the second sample all numbers are divisible by number 1.

In the third sample all numbers are prime, so conditions 1 and 2 are true only for pairs of numbers (1,1), (2,2), (3,3), (4,4), (5,5).

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