Groups

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of testcases.

Then the descriptions of $$$t$$$ testcases follow.

The first line of each testcase contains one integer $$$n$$$ ($$$2 \le n \le 1\,000$$$) — the number of students.

The $$$i$$$-th of the next $$$n$$$ lines contains $$$5$$$ integers, each of them is $$$0$$$ or $$$1$$$. If the $$$j$$$-th integer is $$$1$$$, then the $$$i$$$-th student can attend the lessons on the $$$j$$$-th day of the week. If the $$$j$$$-th integer is $$$0$$$, then the $$$i$$$-th student cannot attend the lessons on the $$$j$$$-th day of the week.

Additional constraints on the input: for each student, at least one of the days of the week is convenient, the total number of students over all testcases doesn't exceed $$$10^5$$$.

Output:

For each testcase print an answer. If it's possible to divide the students into two groups of equal sizes and choose different days for the groups so each student can attend the lesson in the chosen day of their group, print "YES" (without quotes). Otherwise, print "NO" (without quotes).

Sample Input:

2
4
1 0 0 1 0
0 1 0 0 1
0 0 0 1 0
0 1 0 1 0
2
0 0 0 1 0
0 0 0 1 0

Sample Output:

YES
NO

Note:

In the first testcase, there is a way to meet all the constraints. For example, the first group can consist of the first and the third students, they will attend the lessons on Thursday (the fourth day); the second group can consist of the second and the fourth students, and they will attend the lessons on Tuesday (the second day).

In the second testcase, it is impossible to divide the students into groups so they attend the lessons on different days.