   Online JudgeProblem SetAuthorsOnline ContestsUser
Web Board
F.A.Qs
Statistical Charts
Problems
Submit Problem
Online Status
Prob.ID:
Register
Authors ranklist
Current Contest
Past Contests
Scheduled Contests
Award Contest
Register
Language:
Finding Bovine Roots
 Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 4788 Accepted: 1007

Description

The cows are trying to find their roots. They are not so smart as humans when they find square roots, the cows lose the integer portion of their square root calculation. Thus, instead of calculating the square root of 2 to be 1.4142135623730950488016887242096980785696, they deduce that it is 0.4142135623730950488016887242096980785696. The square root of 16 is calculated to be 0 (obviously an error).

The erroneous ciphering does, however, lead to an interesting question. Given a string of digits of length L (1 <= L <= 9), what is the smallest integer whose bovine square root decimal part begins with those digits?

By way of example, consider the string "123". The square root of 17 is approximately 4.1231056256176605498214098559740770251472 so the bovine square root is: 0.1231056256176605498214098559740770251472 whose decimal part (just after the period) starts with 123. It turns out that 17 is the smallest integer with this property.

Input

Line 1: A single integer, L

Line 2: L digits (with no spaces)

Output

Line 1: A single integer that is the smallest integer whose bovine square root starts with the supplied string

Sample Input

```3
123```

Sample Output

`17`

Hint

Be careful of floating point arithmetic. It engenders rounding errors that can be surprising.

Explanation of the sample:

sqrt(17) ~= 4.1231056256176605498214098559740770251472

Source

[Submit]   [Go Back]   [Status]   [Discuss] Home Page Go Back To top