Limits 1s, 512 MB

Have you played the game Spot it!? Though there are many ways to play this game, the basic rule is the same for all - find the matching element between two cards.

In a classic deck of Spot it! there are 55 cards, each containing 8 different symbols. And there is a very interesting property. Any 2 cards have exactly one symbol in common.

This makes many people wonder: how many symbols are sufficient to make those 55 cards?

Let us be more generic and find out:
How many symbols are sufficient to make a deck of N cards?
So that in a deck of N cards:

  • All cards contain the same number of symbols.
  • Any 2 of the cards has exactly 1 symbol in common.
  • Each card has more than 1 symbol and
  • All symbols in a single card are different.


An integer $T$ ($1 \le T \le 100$) denoting the number of test cases to follow.

Each of the next T lines will have an integer $N$ ($1 \le N \le 10^4$).


For each test case, print the minimum number of symbols required in a new line.




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12% Solution Ratio
AmsiamEarliest, Apr '20
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