Whole-Array Assignment Is Not Allowed

Source: C Primer Plus

Version: Phuoc Hung OJ Extended

Problem Statement

In C, an actual array object is not a value that can be assigned as a whole with the = operator after declaration. If a and b are arrays of the same size, a statement such as a = b; is invalid. In contrast, an individual element such as $a_i$ is an ordinary integer object and can be assigned. To copy all elements of b into a, the program must copy the elements individually or use an appropriate library operation.

This task models three operation types on integer arrays $A$ and $B$, each containing $n$ elements indexed from $0$ to $n-1$:

• Type 1 i x: assign $A_i=x$. This assignment is valid and changes $A_i$.
• Type 2: represent an attempted whole-array assignment A = B. This is invalid in C and does not change the simulated data.
• Type 3: copy every element of $B$ into $A$, so after the operation $A_i=B_i$ for all $0\le i<n$. This operation is valid.

For every operation, print whether it is valid. After all operations, print the final state of $A$.

Input

• The first line contains $n$.
• The second line contains $n$ integers $A_0,A_1,\ldots,A_{n-1}$.
• The third line contains $n$ integers $B_0,B_1,\ldots,B_{n-1}$.
• The fourth line contains $q$.
• Each of the next $q$ lines describes one operation in one of the forms 1 i x, 2, or 3. For a type-1 operation, $0\le i<n$ is guaranteed.

Output

For each operation, print one line:

• VALID for an element assignment or an element-by-element copy;
• INVALID_ARRAY_ASSIGNMENT for the attempted A = B operation.

After the $q$ result lines, print A = a0 a1 ... a(n-1) containing the final array $A$.

Subtasks

Subtask 1 (100 points): $1\le n\le1000$, $1\le q\le1000$, $-10^9\le A_i,B_i,x\le10^9$.

Examples

Input

4
1 2 3 4
10 20 30 40
4
1 2 99
2
3
1 0 -5

Output

VALID
INVALID_ARRAY_ASSIGNMENT
VALID
VALID
A = -5 20 30 40

Explanation

Initially $A=(1,2,3,4)$ and $B=(10,20,30,40)$.

Operation 1 2 99 assigns one element, so it is valid and changes $A$ to $(1,2,99,4)$.

Operation 2 represents A = B. Whole-array assignment is invalid in C, so the simulated array does not change.

Operation 3 copies the elements of $B$ one by one, producing $A=(10,20,30,40)$.

Finally, 1 0 -5 sets $A_0=-5$, so the final array is $(-5,20,30,40)$.