Migrated from Lutece 540 SaSet

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Description

Saya defines a set consists of square numbers($\left \{ i\mid i=x^2,x\in N \right \}$ or $\{0,1,4,9,16\cdots\}$) called Saya Set(SaSet for short). The addition on this set is defined by Saya:

$a+0(a\in SaSet)=a$

$a+1(a\in SaSet)=min(\left \{x\mid x>a,x\in SaSet\right \})$

($min(S)$ here is a function which returns the minimum element in the given set $S$. For example, $min(SaSet)=0$.)

Examples:

$0+1=1$, $1+1=4$, $4+1=9\cdots$

$a-0(a\in SaSet)=a$

$a-1(a\in SaSet)=max(\left \{x\mid x<a, x\in SaSet\right \})$

($max(S)$ here is a function which returns the maximum element in the given set $S$.)

Example:

$1-1=0$, $4-1=1$, $9-1=4\cdots$

$a+b(a,b\in SaSet)=a+1+(b-1)$

Example:

$4+4=4+1+(4-1)=9+1=16$

Input

There is only one integer $T$($1\leq T\leq 50$) in the first line, which denotes the number of test cases.

Then T lines follows, each line will consists of two integers $a$ and $b$($0\leq a+b\leq 400$,$a,b\in SaSet$). You are asked to calculate the answer of $a+b$.

Output

For each case, output an integer, which denotes the result of $a+b$ according to the definitions above.

Samples

2
0 0
4 4

0
16

Resources

Saya Mathematics@蒲公英的黄昏