Today your maths teacher has taught you to calculate the number of factors of any number. He has given you assignment to complete. The assignment is based on factor chain. Factor chain can be explained through the following example
Let say we have number 10. Number of factors for 10 are 4 (1, 2, 5, 10). Now our number becomes 4 and number of factors for 4 are 3 (1, 2, 4). Now our number becomes 3 and number of factors for 3 are 2 (1, 3). Now our number becomes 2 and number of factors for 2 are 2 (1, 2). Now here we stop because it goes into infinite loop. So our Factors chain will be
10 -> 4 -> 3 -> 2. The length of the chain is 3.
You are given an array nums of n integers and q queries will be asked to you. The queries are of three types
1) + x, You need to add element x to the array.
2) â 1, You need to remove the number that has longest length of factors chain. If two or more numbers have same length then remove the smallest integer of all that numbers.
3) ? 1, You need to output the number that has longest length of factors chain. If two or more numbers have same length then output the smallest integer of all that numbers.
It is guaranteed that the query has at least 1 query of third type. The 2nd ad 3rd query will always be valid.