Algorithms and Data Structures

  • Profound Academy

    • Status
      • 1
        Implementation
      • 2
        Bitwise operations
      • 3
        Prefix Sums
      • 4
        Sliding window / Two pointers
      • 5
        Modular Arithmetic
      • 6
        Number Theory
      • 7
        Binary Search
      • 8
        Basic Sorting
      • 9
        Greedy Algorithms
      • 10
        Basic Dynamic Programming
      • 11
        Recursion
      • 12
        Linked LIst
      • 13
        Queue & Stack
      • 14
        Binary tree + BST
      • 15
        Divide & Conquer + Advanced Sorting
      • 16
        Heap
      • 17
        Hashing
      • 18
        Graph Representation
      • 19
        BFS

    • Bertrand's postulate

    Bertrand's postulate is a theorem stating that for any integer n > 1, there always exists at least one prime number p that is between n and 2n .
    You are asked to solve a more challenging task. Given a number n, you should answer questions like how many prime numbers p are there such that n < p < 2n.

    Input

    The first line of the input contains a single integer t (1 ≤ t ≤ 100) the number of test cases.
    The next t lines contain a single integer n (2 ≤ n ≤ 500 000).

    Output

    The program should print the number of primes between n and 2n for each test case on separate lines.

    Examples

    Input
    Output
    2 2 239
    1 39
     

    Constraints

    Time limit: 1 seconds

    Memory limit: 512 MB

    Output limit: 1 MB

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