CodeChef : July Challenge 2017 – Chef and Sign Sequences

By | July 8, 2017

Chef and Sign Sequences

Source: CodeChef

Chef and Sign Sequences :

Chef found a strange string yesterday – a string of signs s, where each sign is either a ‘<‘‘=’ or a ‘>’. Let N be the length of this string. Chef wants to insert N + 1 positive integers into this sequence and make it valid. A valid sequence is a sequence where every sign is preceded and followed by an integer, and the signs are correct. That is, if a sign ‘<‘ is preceded by the integer a and followed by an integer b, then a should be less than b. Likewise for the other two signs as well.

Chef can take some positive integers in the range [1, P] and use a number in the range as many times as he wants.

Help Chef find the minimum possible P with which he can create a valid sequence.

Input

The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.

The only line of each test case contains the string of signs s, where each sign is either ‘<‘‘=’ or a ‘>’.

Output

For each test case, output a single line containing an integer corresponding to the minimum possible P.

Constraints

  • 1 ≤ T, |s| ≤ 105
  • 1 ≤ Sum of |s| over all test cases in a single test file ≤ 106

Subtasks

Subtask #1 (30 points)

  • 1 ≤ T, |s| ≤ 103
  • 1 ≤ Sum of |s| over all test cases in a single test file ≤ 104

Subtask #2 (70 points)

  • Original constraints

Example

Input:
4
<<<
<><
<=>
<=<

Output:
4
2
2
3

Explanation

Here are some possible valid sequences which can be formed with the minimum P for each of the test cases:

1 < 2 < 3 < 4
1 < 2 > 1 < 2
1 < 2 = 2 > 1
1 < 2 = 2 < 3

Solution

Tried to solve it.. Passed 1,2,5,6 test cases. I think I am missing some corner case as of now.