I am trying to find a CFG for the language A below. I have spent hours on this but still could not find the answer. I also came up with the idea that this may not a context- free language but there is actually a PDA that recognizes it. I would very much appreciate if anyone can help me with this.

                    A= {0^a 1^b 0^c 1^d | a+b < c+d, a,b,c,d>=1}

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