Non-decreasing

Snuke has an integer sequence, a, of length N. The i-th element of a (1-indexed) is a_{i}.

He can perform the following operation any number of times:

• Operation: Choose integers x and y between 1 and N (inclusive), and add a_x to a_y.

He would like to perform this operation between 0 and 2N times (inclusive) so that a satisfies the condition below. Show one such sequence of operations. It can be proved that such a sequence of operations always exists under the constraints in this problem.

• Condition: a_1 \leq a_2 \leq ... \leq a_{N}

Constraints

• 2 \leq N \leq 50
• -10^{6} \leq a_i \leq 10^{6}
• All input values are integers.

Input

Input is given from Standard Input in the following format:

N a_1 a_2 ... a_{N}

Output

Let m be the number of operations in your solution. In the first line, print m. In the i-th of the subsequent m lines, print the numbers x and y chosen in the i-th operation, with a space in between. The output will be considered correct if m is between 0 and 2N (inclusive) and a satisfies the condition after the m operations.

Examples

Input

3 -2 5 -1

Output

2 2 3 3 3

Input

2 -1 -3

Output

1 2 1

Input

5 0 0 0 0 0

Output

0

inputFormat

input values are integers.

Input

Input is given from Standard Input in the following format:

N a_1 a_2 ... a_{N}

outputFormat

Output

Let m be the number of operations in your solution. In the first line, print m. In the i-th of the subsequent m lines, print the numbers x and y chosen in the i-th operation, with a space in between. The output will be considered correct if m is between 0 and 2N (inclusive) and a satisfies the condition after the m operations.

Examples

Input

3 -2 5 -1

Output

2 2 3 3 3

Input

2 -1 -3

Output

1 2 1

Input

5 0 0 0 0 0

Output

0

样例

3
-2 5 -1

2
2 3
3 3

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