Problem Description

Once upon a time, a rabbit tried to write the first $ N $ rows of Pascal's triangle. Let $ C[i][j] $ be the value written in the $ j $-th position of the $ i $-th row from the top ($0 \le i < N$, $0 \le j \le i$). The rabbit attempted to calculate each $ C[i][j] $ using the following procedure:

for i = 0 to N - 1:
    C[i][0] = C[i][i] = 1
    for j = 1 to i - 1:
        C[i][j] = C[i - 1][j - 1] + C[i - 1][j]

However, the rabbit made exactly one mistake in the addition (in the 4th line of the pseudocode) and ended up with a larger integer than the correct sum.

Furthermore, over time, some of the integers written by the rabbit have disappeared.

You are given integers $ A_{i,j} $ ($0 \le i < N$, $0 \le j \le i$) representing the information about the triangle written by the rabbit.

• When $ A_{i,j} = 0 $, the integer written in the $ j $-th position of the $ i $-th row from the top is unknown.
• When $A_{i,j} \ne 0$, the integer written in the $ j $-th position of the $ i $-th row from the top is $ A_{i,j} $.

Determine which $ (i, j) $ the rabbit made a mistake in the addition (which $ C[i][j] $ calculation). If there are multiple possible $ (i, j) $ or if there is an error and no such $ (i, j) $ exists, report accordingly.

Input Format

$ N $ $ A_{0,0} $ $ A_{1,0} $ $ A_{1,1} $ $\vdots$ $ A_{N-1,0} $ $ A_{N-1,1} $ $\cdots$ $ A_{N-1,N-1} $

Output Format

Output the $ (i, j) $ where the rabbit made a mistake in the addition in the order of $ i $, $ j $. If there are multiple possible $ (i, j) $, output AMBIGUOUS. If no such $ (i, j) $ exists, output IMPOSSIBLE.

Sample Input and Output

Sample Input #1

6
1
1 1
1 0 1
1 3 0 1
1 0 7 0 1
1 0 11 0 6 1

Sample Output #1

3 2

Sample Input #2

4
1
1 1
1 0 1
1 0 0 1

Sample Output #2

AMBIGUOUS

Sample Input #3

4
1
1 1
1 0 1
1 4 5 1

Sample Output #3

IMPOSSIBLE

Notes/Hints

Constraints

• $1 \le N \le 500$.
• $0 \le A_{i,j} \le 10^9$.
• For $i = 0, 1, \ldots, N - 1$, $ A_{i,0} = A_{i,i} = 1 $.

Partial Points

• If you solve the dataset satisfying $N \le 50$, you will be awarded $ 20 $ points.
• If you solve the dataset without additional constraints, you will be awarded an additional $ 80 $ points.

Sample Explanation 1

In this case, the triangle written by the rabbit before the integers disappeared could have been as follows. The rabbit mistakenly calculated $ 2 + 1 $ as $ 4 $ when calculating $ C[3][2] $, so output $ (i, j) = (3, 2) $.

1
1 1
1 2 1
1 3 4 1
1 4 7 5 1
1 5 11 12 6 1

Sample Explanation 2

All the addition places have disappeared, so there is a possibility of error at any location.

Sample Explanation 3

The given triangle is inconsistent with Pascal's triangle, so it is impossible to determine the correct location of the mistake.

见题面 Input 部分

见题面 Output 部分