Problem: Given n, find n consecutive positive integers. However, all numbers must have divisors other than 1 and the number itself.

Hint

In Sample Output 2, 8, 9 and 10 are selected as three consecutive integers.
The second and third lines output 3, as a divisor of 9, and the fourth line outputs 5, as a divisor of 10.



Input

The input is given in the following format.


n


The input meets the following constraints.
1 ≤ n ≤ 1,500

Output

Print the smallest of the n consecutive positive integers you choose on the first line.
Output the divisor for each value from the 2nd line to the n + 1 line.
Any value may be output unless the divisor is 1 or the number itself.
Let x be the number output on the first line, and output the divisor of x + i-2 on the i line.

The output value must not exceed 5,000 digits.

Examples

Input

2


Output

8
2
3


Input

3


Output

8
2
3
5

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

using i64 = int64_t;
using u64 = uint64_t;

u64 arr[] = {
    2,
    3,
    2,
    395069,
    2,
    83,
    2,
    3,
    2,
    7,
    2,
    17,
    2,
    3,
    2,
    11,
    2,
    5,
    2,
    3,
    2,
    103,
    2,
    7,
    2,
    3,
    2,
    5,
    2,
    149,
    2,
    3,
    2,
    4931,
    2,
    643,
    2,
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    2,
    1367,
    2,
    31,
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    17,
    2,
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    7,
    2,
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    3,
    2,
    5,
    2,
    11,
    2,
    3,
    2,
    23,
    2,
    7,
    2,
    3,
    2,
    37861,
    2,
    49549,
    2,
    3,
    2,
    13,
    2,
    5,
    2,
    3,
    2,
    11,
    2,
    29,
    2,
    3,
    2,
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    2,
    157,
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    5,
    2,
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};

int main(){
    u64 n;
    cin >> n;
    u64 ans = 6787988999657777797 + 1;
    cout << ans << endl;
    for(u64 i=0;i<n;++i){
        cout << arr[i] << endl;
    }

    return 0;
}