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Javascript, 242 bytes
minDist=(l,m)=>{let e=0,f=[];l.forEach((g,h)=>{let a=[],c=Number.POSITIVE_INFINITY,d=0;m.forEach((b,k)=>{f.includes([h,k])||a.push([g,b,Math.abs(g-b),h,k])});a.forEach((b,a)=>{b[2]<c&&(c=b[2],d=a)});f.push([a[d][3],a[d][4]]);e+=c});return e};
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