Problem: Let's call an array a_1, a_2, ..., a_m of nonnegative integer numbers good if a_1 + a_2 + ... + a_m = 2⋅(a_1 ⊕ a_2 ⊕ ... ⊕ a_m), where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

For example, array [1, 2, 3, 6] is good, as 1 + 2 + 3 + 6 = 12 = 2⋅ 6 = 2⋅ (1⊕ 2 ⊕ 3 ⊕ 6). At the same time, array [1, 2, 1, 3] isn't good, as 1 + 2 + 1 + 3 = 7 ≠ 2⋅ 1 = 2⋅(1⊕ 2 ⊕ 1 ⊕ 3).

You are given an array of length n: a_1, a_2, ..., a_n. Append at most 3 elements to it to make it good. Appended elements don't have to be different. It can be shown that the solution always exists under the given constraints. If there are different solutions, you are allowed to output any of them. Note that you don't have to minimize the number of added elements!. So, if an array is good already you are allowed to not append elements.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10 000). The description of the test cases follows.

The first line of each test case contains a single integer n (1≤ n ≤ 10^5) — the size of the array.

The second line of each test case contains n integers a_1, a_2, ..., a_n (0≤ a_i ≤ 10^9) — the elements of the array.

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case, output two lines.

In the first line, output a single integer s (0≤ s≤ 3) — the number of elements you want to append.

In the second line, output s integers b_1, ..., b_s (0≤ b_i ≤ 10^{18}) — the elements you want to append to the array.

If there are different solutions, you are allowed to output any of them.

Example

Input


3
4
1 2 3 6
1
8
2
1 1


Output


0

2
4 4
3
2 6 2

Note

In the first test case of the example, the sum of all numbers is 12, and their ⊕ is 6, so the condition is already satisfied.

In the second test case of the example, after adding 4, 4, the array becomes [8, 4, 4]. The sum of numbers in it is 16, ⊕ of numbers in it is 8.

Solution (in PYTHON3):

Solution:
def to_2(x):
    ans = []
    while x > 0:
        ans.append(x % 2)
        x //= 2
    return ans[::-1]

def to_10(arr):
    ans = 0
    cur = 1
    for i in arr:
        ans += i * cur
        cur <<= 1
    return ans

t = int(input())
for kkk in range(t):
    n = int(input())
    a = list(map(int, input().split()))
    #a1 = list(map(to_2, a))
    ss = sum(a)
    xx = 0
    for i in range(n):
        xx ^= a[i]
    xx <<= 1
    ss1 = to_2(ss)
    ss1.reverse()
    xx1 = to_2(xx)
    xx1.reverse()
    kek1 = [0 for i in range(50)]
    kek2 = [0 for i in range(50)]
    kek3 = [0 for i in range(50)]
    cur = 0
    cnt = 0
    while True:
        #print(ss1, xx1)
        sum_is_ended = False
        xor_is_ended = False
        cursum = 0
        curxor = 0
        if (cur >= len(ss1)):
            sum_is_ended = True
            ss1.append(0)
            cursum = 0
        else:
            cursum = ss1[cur]
        if (cur >= len(xx1)):
            xor_is_ended = True
            xx1.append(0)
            curxor = 0
        else:
            curxor = xx1[cur]
        if xor_is_ended and sum_is_ended:
            break
        if cursum == curxor:
            pass
        elif cursum == 1 and curxor == 0:
            kek1[cur] = 1
            if len(xx1) <= cur + 1:
                xx1.append(0)
            xx1[cur + 1] += 1
            xx1[cur + 1] %= 2
            ost = 0
            ss1[cur] += 1
            if ss1[cur] == 2:
                ost = 1
                ss1[cur] = 0
            j = 1
            while ost:
                if len(ss1) <= cur + j:
                    ss1.append(0)
                ss1[cur + j] += 1
                if (ss1[cur +  j] == 2):
                    ost = 1
                    ss1[cur + j] = 0
                    j += 1
                else:
                    break
        else:
            kek2[cur - 1] = 1
            kek3[cur - 1] = 1
            ost = 0
            ss1[cur] = 1
        cur += 1
    print(3)
    print(to_10(kek1), to_10(kek2), to_10(kek3))