Makes me wonder

Algebra Level 5

If a,b,c,da, b, c, d are real values that satisfy the system of equations:

abc+ab+bc+ca+a+b+c=71abc + ab +bc + ca + a + b + c = 71
bcd+bc+cd+db+b+c+d=191bcd + bc + cd + db + b + c + d = 191
cda+cd+da+ac+c+d+a=95cda + cd + da + ac + c + d + a = 95
dab+da+ab+bd+d+a+b=143dab + da + ab + bd + d + a + b = 143

Evaluate the value of abcd+a+b+c+dabcd + a + b + c + d.

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