Migrated from Lutece 584 CBS number

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Description

You are given $M$ numbers. We define $X$ as CBS number if the binary sequence of $X$ contains the binary sequence of any other numbers in these $M$ numbers.

Now can you tell me how many CBS numbers in the range of $[l,r]$.

Input

The first line contains a single integer $T$($T\leq 30$),the number of test cases.

In each test case, its first line contains a number $M$ ($1\leq M\leq 1000$).

In each of next $M$ lines contains a number $x$($1\leq x<2^{63}$).

The last line of each case contains two number $l,r$($1\leq l\leq r<2^{63}$).

Output

Please calculate how many CBS numbers in the range of $[l,r]$.

Samples

1
1
3 
1 100

67

Resources

Sichuan University Programming Contest