1003047803

In Duolingo application, every user earns so-called lingots (=virtual currency), providing he or she learns at least $10$ minutes for $10$ consecutive days. For the first $10$ days a user earns $1$ lingot, $2$ lingots for the next ten-day period, $3$ lingots for the following $10$ days (i.e. for the first $30$ days a user earns $6$ lingots), etc. Find the smallest number of days in which a user can accumulate $1000$ lingots.