Benedek wrote the following $300 $ statements on a piece of paper. $2 | 1!$ $3 | 1! \,\,\, 3 | 2!$ $4 | 1! \,\,\, 4 | 2! \,\,\, 4 | 3!$ $5 | 1! \,\,\, 5 | 2! \,\,\, 5 | 3! \,\,\, 5 | 4!$ $...$ $24 | 1! \,\,\, 24 | 2! \,\,\, 24 | 3! \,\,\, 24 | 4! \,\,\, · · · \,\,\, 24 | 23!$ $25 | 1! \,\,\, 25 | 2! \,\,\, 25 | 3! \,\,\, 25 | 4! \,\,\, · · · \,\,\, 25 | 23! \,\,\, 25 | 24!$ How many true statements did Benedek write down? The symbol | denotes divisibility, e.g. $6 | 4!$ means that $6$ is a divisor of number $4!$.