#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,sse4,popcnt,abm,mmx,avx,avx2")
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using vi=vector<int>;
using pi=pair<int,int>;
#define F(i,a,b) for(int i=(a);i<=(b);i++)
#define G(i,a,b) for(int i=(a);i>=(b);i--)
#define ms(a,b) memset(a,b,sizeof(a))
#define si(a) ((int)(a).size())
#define all(a) (a).begin(),(a).end()
#define fi first
#define se second
#define pb push_back
bool S;
const int mod=998244353;
const int N=3e6+3;
char s[N*2];
std::vector<int> sa_naive(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n);
std::iota(sa.begin(), sa.end(), 0);
std::sort(sa.begin(), sa.end(), [&](int l, int r) {
if (l == r) return false;
while (l < n && r < n) {
if (s[l] != s[r]) return s[l] < s[r];
l++;
r++;
}
return l == n;
});
return sa;
}
std::vector<int> sa_doubling(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n), rnk = s, tmp(n);
std::iota(sa.begin(), sa.end(), 0);
for (int k = 1; k < n; k *= 2) {
auto cmp = [&](int x, int y) {
if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
int rx = x + k < n ? rnk[x + k] : -1;
int ry = y + k < n ? rnk[y + k] : -1;
return rx < ry;
};
std::sort(sa.begin(), sa.end(), cmp);
tmp[sa[0]] = 0;
for (int i = 1; i < n; i++) {
tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
}
std::swap(tmp, rnk);
}
return sa;
}
// SA-IS, linear-time suffix array construction
// Reference:
// G. Nong, S. Zhang, and W. H. Chan,
// Two Efficient Algorithms for Linear Time Suffix Array Construction
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
int n = int(s.size());
if (n == 0) return {};
if (n == 1) return {0};
if (n == 2) {
if (s[0] < s[1]) {
return {0, 1};
} else {
return {1, 0};
}
}
if (n < THRESHOLD_NAIVE) {
return sa_naive(s);
}
if (n < THRESHOLD_DOUBLING) {
return sa_doubling(s);
}
std::vector<int> sa(n);
std::vector<bool> ls(n);
for (int i = n - 2; i >= 0; i--) {
ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
}
std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
for (int i = 0; i < n; i++) {
if (!ls[i]) {
sum_s[s[i]]++;
} else {
sum_l[s[i] + 1]++;
}
}
for (int i = 0; i <= upper; i++) {
sum_s[i] += sum_l[i];
if (i < upper) sum_l[i + 1] += sum_s[i];
}
auto induce = [&](const std::vector<int>& lms) {
std::fill(sa.begin(), sa.end(), -1);
std::vector<int> buf(upper + 1);
std::copy(sum_s.begin(), sum_s.end(), buf.begin());
for (auto d : lms) {
if (d == n) continue;
sa[buf[s[d]]++] = d;
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
sa[buf[s[n - 1]]++] = n - 1;
for (int i = 0; i < n; i++) {
int v = sa[i];
if (v >= 1 && !ls[v - 1]) {
sa[buf[s[v - 1]]++] = v - 1;
}
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
for (int i = n - 1; i >= 0; i--) {
int v = sa[i];
if (v >= 1 && ls[v - 1]) {
sa[--buf[s[v - 1] + 1]] = v - 1;
}
}
};
std::vector<int> lms_map(n + 1, -1);
int m = 0;
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms_map[i] = m++;
}
}
std::vector<int> lms;
lms.reserve(m);
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms.push_back(i);
}
}
induce(lms);
if (m) {
std::vector<int> sorted_lms;
sorted_lms.reserve(m);
for (int v : sa) {
if (lms_map[v] != -1) sorted_lms.push_back(v);
}
std::vector<int> rec_s(m);
int rec_upper = 0;
rec_s[lms_map[sorted_lms[0]]] = 0;
for (int i = 1; i < m; i++) {
int l = sorted_lms[i - 1], r = sorted_lms[i];
int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
bool same = true;
if (end_l - l != end_r - r) {
same = false;
} else {
while (l < end_l) {
if (s[l] != s[r]) {
break;
}
l++;
r++;
}
if (l == n || s[l] != s[r]) same = false;
}
if (!same) rec_upper++;
rec_s[lms_map[sorted_lms[i]]] = rec_upper;
}
auto rec_sa =
sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);
for (int i = 0; i < m; i++) {
sorted_lms[i] = lms[rec_sa[i]];
}
induce(sorted_lms);
}
return sa;
}
int n,sa[N*2],rk[N*2],ht[N*2],mn[22][N*2];
void isa(int n){
static int h[N*2];
vector<int>a=sa_is(vector<int>(s+1,s+n+1),255);
F(i,1,n) sa[i]=a[i-1]+1;
F(i,1,n) rk[sa[i]]=i;
F(i,1,n){
int j=sa[rk[i]-1],k=max(0,h[i-1]-1);
while(i+k<=n&&j+k<=n&&s[i+k]==s[j+k]) k++;
h[i]=ht[rk[i]]=k;
}
F(i,1,n) mn[0][i]=ht[i];
F(j,1,21) F(i,1,n-(1<<j)+1) mn[j][i]=min(mn[j-1][i],mn[j-1][i+(1<<(j-1))]);
}
inline int qry(int l,int r){
int k=__lg(r-l+1);
return min(mn[k][l],mn[k][r-(1<<k)+1]);
}
inline int gl(int x,int y){
int l=1,r=rk[x]-1,ans=rk[x];
while(l<=r){
int mid=(l+r)>>1;
if(qry(mid+1,rk[x])>=y){
ans=mid;
r=mid-1;
}else l=mid+1;
}
return ans;
}
inline int gr(int x,int y){
int l=rk[x]+1,r=n,ans=rk[x];
while(l<=r){
int mid=(l+r)>>1;
if(qry(rk[x]+1,mid)>=y){
ans=mid;
l=mid+1;
}else r=mid-1;
}
return ans;
}
int sum[N*2];
char t[N*4];
int p[N*4];
void init(int n){
int m=n;
G(i,n,1) t[i*2]=s[i];
n=n*2+1;
F(i,1,n) if(i&1) t[i]='#';
int mx=0,ans=0;
F(i,1,n){
if(mx+p[mx]>i) p[i]=min(p[mx*2-i],mx+p[mx]-i);
while(i-p[i]>=1&&i+p[i]<=n&&t[i-p[i]]==t[i+p[i]]){
if(t[i+p[i]]!='#'){
int l=(i-p[i])/2,r=(i+p[i])/2;
if(r-l+1<=m/2){
int p=gl(l,r-l+1),q=gr(l,r-l+1);
ans+=(__int128)(sum[q]-sum[p-1])*(sum[q]-sum[p-1])*(r-l+1)%mod;
if(ans>=mod) ans-=mod;
}
}
p[i]++;
}
if(i+p[i]>mx+p[mx]) mx=i;
}
cout<<ans;
}
bool T;
int main(){
// cerr<<(&S-&T)/1024./1024.;
cin.tie(0)->ios::sync_with_stdio(0);
cin>>n>>(s+1);
// n=3e6; F(i,1,n) s[i]='a';
F(i,1,n) s[i+n]=s[i];
n*=2;
isa(n);
F(i,1,n) sum[i]=sum[i-1]+(sa[i]<=n/2);
init(n);
}