I think first we need to sort the boxes in decreasing order of height , width and length so that input like this (7,8,9),(5,6,8), (5,8,7),(4,4,4),(3,2,1),(9,9,10),(9,3,7) becomes (9,9,10),(9,3,7),(7,8,9),(5,8,7),(5,6,8),(4,4,4),(3,2,1) . Now we can apply DP here . Let dp[i] = maximum no. of boxes fitting into each other such that the i_th box is the last to fit. Then dp[i] = max(dp[j]) +1 , where j<i and wi>wj , hi>hj and li>lj .
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