You are given an array of ** N** positive integers. Find a non-empty subset of numbers from the given array with the property that the sum of all numbers in the subset is divisible by

**.**

`N`### Input

On the first line of the input there will be number ** N**. On the next line there will be

**integer numbers with the semnification above.**

`N`### Output

The number of elements in the solution, ** M**, followed on the second line by

**space separated numbers, denoting the positions of the elements of the input array which form the solution.**

`M`The positions are one-based.

### Constraints

- 1 ≤
≤`N``4 * 10`^{5} - 0 ≤ all elements in the array ≤
`10`^{9} - If there are multiple solutions, output any of them.

### Sample

Input | Output |
---|---|

1010 9 8 4 3 2 5 7 6 1 | 23 6 |

Consider the array of partial sums ** s_{i} = (a_{1} + a_{2} + … + a_{i}) % N, (1 ≤ i ≤ N)**. Clearly, this array contains exactly

**values between**

`N`**and**

`0`**.**

`N-1`If there exists an index ** i** such that

**, then we can construct our subset by choosing all elements**

`s`_{i}= 0**. Otherwise, it follows from Dirichlet's principle that at least one value occurs multiple times. Denote by**

`a`_{j}(1 ≤ j ≤ i)**and**

`i`**two indices such that**

`j`**. Then we can construct our subset by choosing all elements**

`i < j, s`_{i}= s_{j}**.**

`a`_{k}(i < k ≤ j)Note that this solution proves another property of the problem: besides the fact that any array of size ** N** contains at least one subset whose sum is divisible by

**, it also contains at least one such subset that is also a continuous subsequence of the array.**

`N`