#define PROBLEM "https://judge.yosupo.jp/problem/many_factorials"

#pragma GCC optimize("Ofast,unroll-loops")

#include <bits/stdc++.h>

#include "blazingio/blazingio.min.hpp"

#include "cp-algo/util/simd.hpp"

#include "cp-algo/math/common.hpp"

using namespace std;

using namespace cp_algo;

constexpr int mod = 998244353;

constexpr auto mod4 = u64x4() + mod;

constexpr auto imod4 = u64x4() - math::inv2(mod);

void facts_inplace(vector<int> &args) {

constexpr int block = 1 << 16;

static basic_string<size_t> args_per_block[mod / block];

uint64_t limit = 0;

for(auto [i, x]: args | views::enumerate) {

if(x < mod / 2) {

limit = max(limit, uint64_t(x));

args_per_block[x / block].push_back(i);

} else {

limit = max(limit, uint64_t(mod - x - 1));

args_per_block[(mod - x - 1) / block].push_back(i);

}

}

uint64_t b2x32 = (1ULL << 32) % mod;

uint64_t fact = 1;

for(uint64_t b = 0; b <= limit; b += block) {

u64x4 cur = {b, b + block / 4, b + block / 2, b + 3 * block / 4};

static array<u64x4, block / 4> prods;

prods[0] = u64x4{cur[0] + !b, cur[1], cur[2], cur[3]};

cur = cur * b2x32 % mod;

for(int i = 1; i < block / 4; i++) {

cur += b2x32;

cur = cur >= mod ? cur - mod : cur;

prods[i] = montgomery_mul(prods[i - 1], cur, mod4, imod4);

}

for(auto i: args_per_block[b / block]) {

size_t x = args[i];

if(x >= mod / 2) {

x = mod - x - 1;

}

x -= b;

auto pre_blocks = x / (block / 4);

auto in_block = x % (block / 4);

auto ans = fact * prods[in_block][pre_blocks] % mod;

for(size_t z = 0; z < pre_blocks; z++) {

ans = ans * prods.back()[z] % mod;

}

if(args[i] >= mod / 2) {

ans = math::bpow(ans, mod - 2, 1ULL, [](auto a, auto b){return a * b % mod;});

args[i] = int(x % 2 ? ans : mod - ans);

} else {

args[i] = int(ans);

}

}

args_per_block[b / block].clear();

for(int z = 0; z < 4; z++) {

fact = fact * prods.back()[z] % mod;

}

}

}

void solve() {

int n;

cin >> n;

vector<int> args(n);

for(auto &x : args) {cin >> x;}

facts_inplace(args);

for(auto it: args) {cout << it << "\n";}

}

signed main() {

//freopen("input.txt", "r", stdin);

ios::sync_with_stdio(0);

cin.tie(0);

int t = 1;

//cin >> t;

while(t--) {

solve();

}

}