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You are given non-negative integers $A,B,C$.

Define a sequence $X=(X_1,X_2,\cdots,X_{A+B+C})$ of length as follows.

You may perform the following operation any number of times: choose two distinct indices $i,j$ and replace both $X_i$ and $X_j$ with .

Find the minimum number of operations required to make all elements of $X$ equal, and output one sequence of operations attaining the minimum. If it is impossible, print $-1$.

If it is possible, it can be proven that under the given constraints, the minimum number of operations is always at most $10^7$.

Partial scoring is available for this problem. See the Scoring section for details.

The input is given from Standard Input in the following format:

$A\ B\ C$

If it is impossible, print $-1$ on one line.

Otherwise, first print the minimum number of operations $K$. Then print $K$ lines; on the $t$-th line, print the two indices $i_t,j_t$ chosen in the -th operation, in the following format:

• $A,B,C \ge 0$.
• $1 \le A+B+C \le 500\,000$.

The score for each test case, as a percentage of the score of the subtask containing it, is calculated as follows.

If it is impossible to make all elements equal:

• If you print $-1$, the score is $100\%$.
• Otherwise, the score is $0\%$.

If it is possible to make all elements equal:

• If you print $-1$, the score is $0\%$.