Some positive integers are initially written on a board, where each 2 of them are different. Each time we can do the following moves:  
1. If there are 2 numbers (written on the board) in the form $n, n+1$, we can erase them and write down $n-2$.  
2. If there are 2 numbers (written on the board) in the form $n, n+4$, we can erase them and write down $n-1$.  

After some moves, there might appear negative numbers. Find the maximum value of the integer $c$ such that independently of the starting numbers, each number which appears in any move is greater than or equal to $c$.

Let's think step by step and output the final answer within \boxed{}.
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