# Count The Blocks

You wrote down all integers from $0$ to $10^n – 1$, padding them with leading zeroes so their lengths are exactly $n$. For example, if $n = 3$ then you wrote out 000, 001, …, 998, 999.

A block in an integer $x$ is a consecutive segment of equal digits that cannot be extended to the left or to the right.

For example, in the integer $00027734000$ there are three blocks of length $1$, one block of length $2$ and two blocks of length $3$.

For all integers $i$ from $1$ to $n$ count the number of blocks of length $i$ among the written down integers.

Since these integers may be too large, print them modulo $998244353$.

Input

The only line contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$).

Output

In the only line print $n$ integers. The $i$-th integer is equal to the number of blocks of length $i$.

Since these integers may be too large, print them modulo $998244353$.

Examples

input

1


output

10


input

2


output

180 10

Solution:

#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
mt19937 mrand(random_device{}());
const ll mod=998244353;
int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}

int n;
ll pw[201000];
int main() {
scanf("%d",&n);
pw[0]=1;
for (int i=1;i<=n;i++) pw[i]=pw[i-1]*10%mod;
for (int i=1;i<=n;i++) {
if (i==n) { puts("10"); continue; }
int d=0;
if (i<=n-2) d=(d+10*(n-i-1)*9*9*pw[n-i-2])%mod;
d=(d+2*10*9*pw[n-i-1])%mod;
printf("%d ",d);
}
}