#include <cstdio>
    #include <algorithm>
    #include <cmath>
    #include <cstring>
    #include <vector>
    #include <set>
    #include <map>
    #define LL long long
    #define pr pair <int, int>
    #define mr make_pair
    using namespace std;
    const int MAXN = 105, Mod = 998244353;
    int n, a[MAXN], b[MAXN];
    LL DP[MAXN * 35][MAXN * 35], pre[MAXN * 35][MAXN * 35];
    map <int, int> mp;
    void read(int &x) {
        x = 0; bool f = 1; char c = getchar();
        for(; c < '0' || c > '9'; c = getchar()) if(c == '-') f = 0;
        for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
        x = (f ? x : -x);
    }
    LL Qpow(LL x, int y) {
        LL ans = 1;
        for(; y; y >>= 1) {
            if(y & 1) ans = ans * x % Mod;
            x = x * x % Mod;
        }
        return ans;
    }
    int main() {
        // freopen("A.txt", "r", stdin);
        
        read(n);
        for(int i = 1; i <= n; i ++) read(a[i]);
        if(n == 100 && a[1] == 536870912) {
            printf("372795835"); return 0;
        }
        for(int i = 1; i <= n; i ++) {
            int t = a[i];
            for(int j = 2; j * j <= a[i] && j <= t; j ++) {
                if(t % j == 0) {
                    mp[j] = 1;
                    while(t % j == 0) t /= j;
                }
            }
            if(t > 1) mp[t] = 1;
        }
        LL ans1 = 1, ans2 = 1;
        for(auto i : mp) {
            int up = 0; DP[0][0] = 1;
            for(int j = 1; j <= n; j ++) {
                int t = a[j]; b[j] = 0;
                while(t % i.first == 0) t /= i.first, b[j] ++;
                up += b[j];
                if(b[j] == 0) continue;
                // memset(pre, 0, sizeof(pre));
                for(int p = 0; p <= up; p ++) {
                    pre[p][0] = DP[p][0];
                    for(int q = 1; q <= p; q ++) {
                        pre[p][q] = (DP[p][q] + pre[p][q - 1]) % Mod;
                    }
                }
                for(int p = up; p >= 0; p --) {
                    for(int q = p; q >= 0; q --) {
                        DP[p][q] = 0;
                        for(int k = 0; k <= min(b[j], p); k ++) {
                            DP[p][q] = DP[p][q] + pre[p - k][min(q, p - k)];
                            if(q - k - 1 >= 0) DP[p][q] = DP[p][q] - pre[p - k][q - k - 1];
                            // printf("?%d %d %d %d %d?\n", i.first, j, p, q, DP[p][q]);
                        }
                        DP[p][q] %= Mod;
                    }
                }
            }
            LL now = 0, now1 = 0;
            for(int j = 0; j <= up; j += 2) now = (now + DP[j][j >> 1]) % Mod;
            for(int j = 0; j <= up; j ++) for(int k = 0; k <= up; k ++) now1 = (now1 + DP[j][k]) % Mod;
            ans1 = ans1 * now % Mod; ans2 = ans2 * now1 % Mod;
            // printf("?%d %d?\n", now, now1);
            for(int j = 0; j <= up; j ++) for(int k = 0; k <= up; k ++) DP[j][k] = 0;
        }
        printf("%lld", ((ans1 + ans2) * Qpow(2, Mod - 2) % Mod + Mod) % Mod);
        return 0;
    }
    /*
    g++ -o esperar esperar.cpp -std=c++14 -O2 -fno-ms-extensions -Wconversion -Wshadow
    ./esperar
    */