题目描述

Let's call an array a consisting of n positive (greater than 0) integers beautiful if the following condition is held for every i from 1 to n: either $a_i$=1, or at least one of the numbers $a_i$−1 and $a_i$−2 exists in the array as well.

For example:

• the array [5,3,1] is beautiful: for $a_1$, the number $a_1$−2=3 exists in the array; for $a_2$, the number $a_2$−2=1 exists in the array; for $a_3$, the condition $a_3$=1 holds;
• the array [1,2,2,2,2] is beautiful: for $a_1$, the condition $a_1$=1 holds; for every other number $a_i$, the number $a_i$−1=1 exists in the array;
• the array [1,4] is not beautiful: for $a_2$, neither $a_2$−2=2 nor $a_2$−1=3 exists in the array, and $a_2$≠1;
• the array [2] is not beautiful: for $a_1$, neither $a_1$−1=1 nor $a_1$−2=0 exists in the array, and $a_1$≠1;
• the array [2,1,3] is beautiful: for $a_1$, the number $a_1$−1=1 exists in the array; for $a_2$, the condition $a_2$=1 holds; for $a_3$, the number $a_3$−2=1 exists in the array. You are given a positive integer s. Find the minimum possible size of a beautiful array with the sum of elements equal to s.

输入格式

The first line contains one integer t (1≤t≤5000) — the number of test cases.

Then t lines follow, the i-th line contains one integer s (1≤s≤5000) for the i-th test case.

输出格式

Print t integers, the i-th integer should be the answer for the i-th testcase: the minimum possible size of a beautiful array with the sum of elements equal to s.

样例

4 
1 
8 
7 
42 

1 
3 
3 
7 

提示

Consider the example test:

1. in the first test case, the array [1] meets all conditions;
2. in the second test case, the array [3,4,1] meets all conditions;
3. in the third test case, the array [1,2,4] meets all conditions;
4. in the fourth test case, the array [1,4,6,8,10,2,11] meets all conditions.

By 夏夜