Let \(u_n(t)\), \(n=1,2…\) be a sequence of concave functions on \(\mathbb{R}\). Let \(g(t)\) be a differentiable function on \(\mathbb{R}\). Assume \(\liminf_{n\to\infty} u_n(t) \geq g(t)\) for every \(t\) and \(\lim_{n\to \infty} u_n(0) = g(0)\). Suppose \(u_n'(0)\) exist for \(n=1,2,…\). Compare \(\lim_{n\to \infty} u_n'(0)\) and \(g'(0)\).

Count the number of distinct matrices \( A \), where two matrices are considered identical if one can be obtained from the other by rearranging rows and columns, that have the following properties:

1. \( A \) is a \( 7 \times 7 \) matrix and every entry of \( A \) is \( 0 \) or \( 1 \).
2. Each row of \( A\) contains exactly 3 non-zero entries.
3. For any two distinct rows \( i\) and \( j\) of \( A\), there exists exactly one column \( k \) such that \( A_{ik} \neq 0 \) and \( A_{jk} \neq 0 \).