Saaho and Dream Girl clashes at the box office.Saaho is a big budget movie as compared to Dream girl So Saaho started well at the Box office. Total collections of Saaho at the end of \(N\)^th day at the box office is given by \(A^N\).As the review of Dream Girl is positive, Its collection pick up day by day and the total collections of Dream Girl at the end of \(N\)^th day at the box office is given by \(N!\). Find minimum number of days at the box office in which Dream girl collection crosses the Saaho collection.

Input
The first line of the input contains number \(T (1<=T<=10^5)\), the number of testcases.
Each test case consists of a single number \(A (2<=A<=10^6)\).

Output
For each test cases print the minimum number of days in new line.