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Iodine supplements are unnecessary.
Just include konbu (kelp) in your diet. You don't even need that much. I cut off an inch or two and use it to make a soup base every day. Has more than enough of your daily needed intake of iodine.
If your diet isn't dogshit, you should have sufficient nutrients needed to metabolize iodine from the foods you eat. Or just eat a Japanese diet. Hypothyroidism is basically non existent here, unlike in the US where every woman makes weekly visits to their endocrinologist.