Draw a table with \(n+1\) columns and \(n\) rows, such that each column contains the numbers \(1,2,3,\cdots, n\). Explain how this table can be used to give a visual proof of the following identity \[(1^1\times 1!)\times (2^2\times 2!)\times (3^3\times 3!)\times\cdots \times (n^n\times n!)=(n!)^{n+1}\]