Input Format The first line of input contains a positive integer T denoting the number of test cases that follow. Each test case is described in a single line containing a single integer N denoting the number of ice cream bars you have. Output Format For each test case, output a single line containing the number of days you can eat for before running out of ice cream bars and not being able to fully eat the next day. Constraints 1 s T ≤ 100 Main Test Set 1 ≤N≤ 105 Bonus Test Set 1 1 ≤N≤ 10¹5 Careful! If you are a Java or C/C++ programmer, be aware that the int variable type may be too small to contain N! Java programmers can use variable types long or float instead, and likewise long long or float for C/C++. Bonus Test Set 2 1sN≤ 1010000 Careful! Values of N in this test set are extremely large! They exceed the maximum values of 64 bit integers and floats. This one can be quite tricky to get right, so we recommend trying other problems first if you're stuck. Sample Test Cases Sample Input 0 1 2 3 6 11 69 1337 12345 Sample Explanations Sample Output 0 1 1 2 3 4 11 51 156 For test case 1, For test case 1, you have no ice cream bars. You can't eat any at all. Thus, you can only eat for 0 days. For test case 2, you have 1 ice cream bar. You eat your only bar on day 1, and then won't have enough for day 2. Thus, you can only eat for 1 days. For test case 3, you have 2 ice cream bars. You eat your first bar on day 1, and then won't have enough for day 2 because you need 2 but only have 1 more. Thus, you can only eat for 1 day. For test case 4, you have 3 ice cream bars. You eat your first bar on day 1, and then your last 2 bars on day 2. You won't have enough for day 3. Thus, you can eat for 2 days. For test case 5, you have 6 ice cream bars. You eat 1 bar on day 1, 2 bars on day 2, and 3 bars on day 3. You won't have enough for day 4. Thus, you can eat for 3 days. For test case 6, you have 11 ice cream bars. You eat 1 bar on day 1, 2 bars on day 2, 3 bars on day 3, and 4 bars on day 4. Since you only have 1 left, you won't have enough for day 5. Thus, you can eat for 4 days.