D. Dice Game - Finding the Minimum Moves to Reach a Target Sum

To solve this problem, we can observe that the sum of the spots on opposite sides of the dice is always 7. Therefore, if the required sum is greater than 6, it is not possible to reach that sum using the dice.

For a required sum less than or equal to 6, we can calculate the number of moves needed as follows:

1. Subtract 1 from the required sum to account for the initial move that doesn't add any value.
2. Divide the remaining sum by 6 to get the number of complete rotations needed.
3. If there is a remainder, add 1 to the number of rotations needed.

Here is the implementation in Python:

t = int(input())

for _ in range(t):
    n = int(input())
    
    if n > 6:
        print(-1)
    else:
        moves = (n - 1) // 6 + 1
        print(moves)

This solution has a time complexity of O(1) as it only requires a few arithmetic operations for each test case.