item/item suggests that you can build these and their pieces in whatever order fits the game. Sell avarice blades as needed after IE but make sure to keep crit up.
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You should also know that you aren't very strong early game unless you get some lucky crits. Also you will probably eat a lot of CC all game and be frustrated. Jungling whatever is very easy after BF. IE hopefully comes somewhere around ~20 depending on last hitting and kills.