Pair of Numbers

Pair of Numbers

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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思路很简单，就是枚举。从左到右开始不断地枚举。但是如果只是这样的话，肯定会超时的。于是就想着“剪枝” 把没有必要再遍历的就直接跳过。通过发现，公因数是几个数里面最小的那个。从左到右遍历，每次都以枚举点为中心向两边取余，结束后（不能整除时）把i直接跳到取余时所到达的最右边。即 i=i+lenL; 这行代码最为重要。节省了大量的时间