Remove redundant brackets. Clean up lists

Question

There are numerous examples whose end result is the removal of empty brackets "{}" and empty lists here, I still can't find an example of simply removing redundant brackets though.

(It's hard for me to believe there isn't already a common solution to this problem. Please point me there if I missed it. As I am new to mathematica I am learning primarily by example so when I ran into this problem I was at a loss of where to even start.The column like formatting is unique to this question, and is for visual aid only. The actual input is at the bottom.)

For example I have this list as INPUT to a new function:

{
{{{0, 5}, {1, 4}, {2, 3}, {3, 2}, {4, 1}, {5, 0}}},
{{{1, 5}, {2, 4}, {3, 3}, {4, 2}, {5, 1}}},
{{{2, 5}, {3, 4}, {4, 3}, {5, 2}}},
{{{3, 5}, {4, 4}, {5, 3}}},
{{{4, 5}, {5, 4}}},
{{{5, 5}}, {{5, 5}}}
}

I would like the new function to generate this list as OUTPUT:

{
{{0, 5}, {1, 4}, {2, 3}, {3, 2}, {4, 1}, {5, 0}},
{{1, 5}, {2, 4}, {3, 3}, {4, 2}, {5, 1}},
{{2, 5}, {3, 4}, {4, 3}, {5, 2}},
{{3, 5}, {4, 4}, {5, 3}},
{{4, 5}, {5, 4}},
{{5, 5}, {5, 5}}
}

---

The actual input TO new function:

{{{{0, 5}, {1, 4}, {2, 3}, {3, 2}, {4, 1}, {5, 0}}}, {{{1, 5}, {2, 4}, {3, 3}, {4, 2}, {5, 1}}}, {{{2, 5}, {3, 4}, {4, 3}, {5, 2}}}, {{{3, 5}, {4, 4}, {5, 3}}}, {{{4, 5}, {5, 4}}}, {{{5, 5}}, {{5, 5}}}}

The actual output FROM new function:

{{{0, 5}, {1, 4}, {2, 3}, {3, 2}, {4, 1}, {5, 0}}, {{1, 5}, {2, 4}, {3, 3}, {4, 2}, {5, 1}}, {{2, 5}, {3, 4}, {4, 3}, {5, 2}}, {{3, 5}, {4, 4}, {5, 3}}, {{4, 5}, {5, 4}}, {{5, 5}, {5, 5}}}

Answer 1

Starting with:

a = {{{{0, 5}, {1, 4}, {2, 3}, {3, 2}, {4, 1}, {5, 0}}}, {{{1, 5}, {2, 4}, {3, 3}, {4, 
      2}, {5, 1}}}, {{{2, 5}, {3, 4}, {4, 3}, {5, 2}}}, {{{3, 5}, {4, 4}, {5, 3}}}, {{{4, 
      5}, {5, 4}}}, {{{5, 5}}, {{5, 5}}}};

This is probably the simplest:

a //. {x_List} :> x