Kulyash believes in equality.
Given an integer N, output a binary string of length N such that:
The count of 01 [subsequences] in the string is equal to the count of 10 subsequences;
The string has at least one occurrence of 0 as well as 1.

If multiple such strings exist, print any. Also, it is guaranteed that corresponding to the given input, an answer always exists.

------ Input Format ------

• First line will contain T, number of test cases. Then the test cases follow.
• Each test case contains of a single line of input, an integer N - the length of the binary string.

------ Output Format ------

For each test case, output any binary string of length N satisfying the given conditions.

------ Constraints ------

$1 ≤ T ≤ 100$
$3 ≤ N ≤ 1000$

----- Sample Input 1 ------
2
4
3

----- Sample Output 1 ------
1001
010

----- explanation 1 ------
Test case $1$: A binary string satisfying both the conditions is $1001$. The count of $01$ as well as $10$ subsequences in the string is $2$.

Test case $2$: A binary string satisfying both the conditions is $010$. The count of $01$ as well as $10$ subsequences in the string is $1$.

见题面

见题面