/*
Problem : A. 乘积，欧拉函数，求和
Url : https://qoj.ac/contest/1840/problem/9619
Date : 2024/11/12 16:19:40
Solver : pmt2018
*/

#include<bits/stdc++.h>

#define y0 pmtx
#define y1 pmtxx
#define x0 pmtxxx
#define x1 pmtxxxx
#define pb push_back
#define mp make_pair
#define fi first 
#define se second
#define lowbit(x) (x&(-x))

#define DEBUG printf("Passing Line %d in function [%s].\n",__LINE__,__FUNCTION__)

using namespace std;

typedef pair<int ,int > pii;
typedef vector<int > vi;
typedef long long ll;
typedef unsigned long long ull;

namespace FastIO{
    const int SIZE=(1<<20);
    char in[SIZE],*inS=in,*inT=in+SIZE;
    inline char Getchar(){
        if(inS==inT){inT=(inS=in)+fread(in,1,SIZE,stdin);if(inS==inT)return EOF;}
        return *inS++;
    }
    char out[SIZE],*outS=out,*outT=out+SIZE;
    inline void Flush(){fwrite(out,1,outS-out,stdout);outS=out;}
    inline void Putchar(char c){*outS++=c;if(outS==outT)Flush();}
    struct NTR{~NTR(){Flush();}}ZTR;
}

#ifndef LOCAL
    #define getchar FastIO::Getchar
    #define putchar FastIO::Putchar 
#endif

template<typename T> inline void read(T &x){
    x=0;int f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9')x=(x<<3)+(x<<1)+ch-'0',ch=getchar();
    x*=f;
}

inline void readstr(char* str){
    int len=0;char c=getchar();
    while(c==' '||c=='\n')c=getchar();
    while(c!=' '&&c!='\n'&&c!='\r')str[len++]=c,c=getchar();
    str[len] = '\0';
}

template<typename T>inline void write(T x){
    if(!x)putchar('0');
    if(x<0)x=-x,putchar('-');
    static int sta[20];int tot=0;
    while(x)sta[tot++]=x%10,x/=10;
    while(tot)putchar(sta[--tot]+48);
}

inline void writestr(char* str){int cur=0;while(str[cur])putchar(str[cur++]);}

const int maxn=200007,INF=0x3f3f3f3f;
const ll MOD=998244353;
const ll LINF=0x3f3f3f3f3f3f3f3fll;
const ll P=19260817;

template<typename T>inline void ckmax(T &x,T y){x=(y>x?y:x);}
template<typename T>inline void ckmin(T &x,T y){x=(y<x?y:x);}
template<typename T>inline T my_abs(T x){if(x<0)x=-x;return x;}
inline int mod1(int x){return x<MOD?x:x-MOD;}
inline int mod2(int x){return x<0?x+MOD:x;}
inline void add(int &x,int y){x=mod1(x+y);}
inline void sub(int &x,int y){x=mod2(x-y);}

int n, a[maxn];

int N=3000;
bool vis[maxn];
int num[maxn],tot;
int big[maxn],pr[maxn];
// vector<int > pr;
vector<int > fr[maxn];
int to[57];
int mask[maxn];
int cnt[maxn][20];
void init_prime(){
    to[2]=0,to[3]=1,to[5]=2,to[7]=3,to[11]=4;
    to[13]=5,to[17]=6,to[19]=7,to[23]=8,to[29]=9;
    to[31]=10,to[37]=11,to[41]=12,to[43]=13,to[47]=14;
    for(int i=2;i<=N;i++){
        if(!vis[i]){
            pr[tot]=i,num[i]=tot++;
            for(int j=i;j<=N;j+=i){
                if(j!=i)vis[j]=true;
                fr[j].pb(i);
            }
        }
    }
    for(int i=2;i<=N;i++){
        for(int x:fr[i]){
            if(x<=47){
                int cur=i;
                while(cur%x==0){
                    cnt[i][to[x]]++;
                    cur/=x;
                }
                if(cnt[i][to[x]]&1)mask[i]|=(1<<to[x]);
            }
            else big[i]=x;
        }
    }
}

int pre[1<<15];
int frac[maxn], ifrac[maxn], inv[maxn];
int qpow(int a, int b) {
    int ret = 1;
    while(b) {
        if(b&1)ret=1ll*ret*a%MOD;
        b>>=1;
        a=1ll*a*a%MOD;
    }
    return ret;
}
void init_pre(){
    frac[0] = 1;
    for (int i = 1; i <= N; i++) frac[i] = 1ll * frac[i-1] * i % MOD;
    ifrac[N] = qpow(frac[N], MOD - 2);
    for (int i = N; i >= 1; i--) {
        ifrac[i - 1] = 1ll * i * ifrac[i] % MOD;
        inv[i] = 1ll * ifrac[i] * frac[i - 1] % MOD;
    }

    pre[0] = 1; 
    for(int s = 1; s < (1 << 15); s++) {
        pre[s] = 1;
        for(int i = 0; i < 15; i ++) {
            if(s & (1<<i)) 
                pre[s] = 1ll * pre[s] * (pr[i] - 1) % MOD * inv[pr[i]] % MOD;
        }
    }
}

int dp[1<<15];
int tmp[1<<15];

int ndp[2][1<<15], ntmp[2][1<<15];

void solve(int bigp) {
    for(int s = 0; s < (1 << n); s++) ndp[0][s] = dp[s];
    for(int i = 1; i <= n; i++) {
        // cout<<big[i]<<endl;
        if(big[a[i]] != bigp) continue;
        for(int s = 0; s < (1 << 15); s ++) 
            ntmp[0][s] = ndp[0][s], ntmp[1][s] = ndp[1][s];
        for(int s = 0; s < (1 << n); s++){
            int ns = s | mask[a[i]];
            int nw = ns ^ s;
            add(ntmp[1][ns], 1ll * ndp[1][s] * a[i] % MOD * pre[nw] % MOD);
            add(ntmp[1][ns], 1ll * ndp[0][s] * a[i] % MOD * pre[nw] % MOD
                                 * (bigp - 1) % MOD * inv[bigp] % MOD);
        }
        for(int s = 0; s < (1 << 15); s ++) 
            ndp[0][s] = ntmp[0][s], ndp[1][s] = ntmp[1][s];
    }
    for(int s = 0; s < (1 << n); s++) dp[s] = mod1(ndp[0][s] + ndp[1][s]);
}

int main(){
    init_prime();
    init_pre();
    read(n);
    for(int i = 1; i <= n; i++) {
        read(a[i]);
    }
    dp[0] = 1;
    for(int i = 1; i <= n; i++) {
        if(!big[a[i]]) {
            // cout<<a[i]<<' ' << bitset<5>(mask[a[i]])<<endl;
            for(int s = 0; s < (1 << 15); s ++) tmp[s] = dp[s];
            for(int s = 0; s < (1 << 15); s ++) {
                int ns = s | mask[a[i]];
                int nw = ns ^ s;
                add(tmp[ns], 1ll * dp[s] * a[i] % MOD * pre[nw] % MOD);
            }
            for(int s = 0; s < (1 << 15); s ++) dp[s] = tmp[s]; 
        }
    }

    for(int b = 15; b < tot; b ++) {
        solve(pr[b]);
    }

    int ans = 0;
    for(int s = 0; s < (1 << 15); s ++) {
        add(ans, dp[s]);
    }
    printf("%d", ans);
    return 0;
}

//things to remember
//1.long long
//2.array length
//3.freopen
//4 boarder case