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: Help Simon, find the required pair of numbers (l, r). If there are multiple required pairs find all of them. The first line contains integer n (1 ≤ n ≤ 3 ·105). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 106). 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. 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).