#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;


int N;
vector<int> A;

void brute() {
  vector<Mint> dp(N + 1, 0);
  dp[0] = 1;
  for (int i = 0; i < N; ++i) {
    int mx = 0;
    for (int j = i + 1; j <= N; ++j) {
      chmax(mx, A[j - 1]);
      if (mx <= j - i) dp[j] += dp[i];
    }
  }
  cerr << A << ": " << dp << endl;
}

namespace easy {
vector<Mint> dp;
vector<int> mxs;
vector<char> on;
vector<vector<int>> iss;
void init() {
  dp.assign(N + 1, 0);
  dp[0] = 1;
  mxs.resize(N + 1);
  on.resize(N + 1);
  iss.resize(N + 1);
}
void rec(int l, int r) {
  if (l + 1 == r) {
    if (A[l] <= 1) dp[r] += dp[l];
  } else {
    // dp[l, mid) -> dp(mid, r]
    const int mid = (l + r) / 2;
    rec(l, mid);
    
    mxs[mid] = 2;
    for (int i = mid; --i >= l; ) mxs[i] = max(A[i], mxs[i + 1]);
    for (int j = mid; j < r; ++j) mxs[j + 1] = max(mxs[j], A[j]);
    /*
      condition for i->j: max{mxs[i], mxs[j]} <= j - i
        - mxs[i] <= j - i  <=>  i + mxs[i] <= j
        - mxs[j] <= j - i  <=>  i <= j - mxs[j]
        i + mxs[i], j - mxs[j]: almost decreasing
    */
    for (int j = mid + 1; j <= r; ++j) iss[j].clear();
    for (int i = l; i < mid; ++i) {
      on[i] = 0;
      if (i + mxs[i] <= r) iss[max(i + mxs[i], mid + 1)].push_back(i);
    }
    // valid: l <= i < k (<= mid)
    Mint now = 0;
    for (int k = l, j = mid + 1; j <= r; ++j) {
      for (const int i : iss[j]) {
        on[i] = 1;
        if (i < k) now += dp[i];
      }
      for (; k < mid && k <= j - mxs[j]; ++k) if (on[k]) now += dp[k];
      for (; k > l && !(k - 1 <= j - mxs[j]); --k) if (on[k - 1]) now -= dp[k - 1];
      dp[j] += now;
    }
    
    rec(mid, r);
  }
}
}  // easy

vector<Mint> pre, suf;

namespace hard {
vector<Mint> diff;
vector<int> mxs;
vector<pair<int, int>> mxss[2];
vector<char> on;
vector<vector<int>> jss, iss;
void init() {
  diff.assign(N, 0);
  mxs.resize(N + 1);
  for (int s = 0; s < 2; ++s) mxss[s].resize(N + 1);
  on.resize(N + 1);
  jss.resize(N + 1);
  iss.resize(N + 1);
}
void rec(int l, int r) {
  if (l + 1 == r) {
    if (A[l] > 1) diff[l] += pre[l] * suf[r];
  } else {
    /*
      diff[h] -= pre[i] suf[j]
        - l <= i < mid < j <= r
        - i <= h < j
        - max{mxs[i], mxs[j]} <= j - i
      diff[h] += pre[i] suf[j]
        - l <= i < mid < j <= r
        - i <= h < j
        - max{mxs'[h][i], mxs'[h][j]} <= j - i
            mxs'[h]: mxs when A[i] <- 1
            at most one h can change each mxs[i] or mxs[j]
    */
    const int mid = (l + r) / 2;
    rec(l, mid);
    
    mxss[0][mid] = mxss[1][mid] = make_pair(2, -1);
    for (int i = mid; --i >= l; ) {
      pair<int, int> tmp(A[i], i);
      for (int s = 0; s < 2; ++s) {
        mxss[s][i] = mxss[s][i + 1];
        if (mxss[s][i] < tmp) swap(mxss[s][i], tmp);
      }
    }
    for (int j = mid; j < r; ++j) {
      pair<int, int> tmp(A[j], j);
      for (int s = 0; s < 2; ++s) {
        mxss[s][j + 1] = mxss[s][j];
        if (mxss[s][j + 1] < tmp) swap(mxss[s][j + 1], tmp);
      }
    }
    // i <= h <= mid
    for (int s = 0; s < 2; ++s) {
      for (int j = mid; j <= r; ++j) mxs[j] = mxss[0][j].first;
      for (int i = mid - 1; i >= l; --i) mxs[i] = mxss[s][i].first;
      for (int i = mid - 1; i >= l; --i) iss[i].clear();
      for (int j = r; j > mid; --j) {
        on[j] = 0;
        if (l <= j - mxs[j]) jss[min(j - mxs[j], mid - 1)].push_back(j);
      }
      // valid: (mid <=) k < j <= r
      Mint now = 0;
      for (int k = r, i = mid - 1; i >= l; --i) {
        for (const int j : jss[i]) {
          on[j] = 1;
          if (j > k) now += suf[j];
        }
        for (; k > mid && k >= i + mxs[i]; --k) if (on[k]) now += suf[k];
        for (; k < r && !(k + 1 >= i + mxs[i]); ++k) if (on[k + 1]) now -= suf[k + 1];
        const int h = mxss[0][i].second;
// if(l<=h&&h<mid)cerr<<"l="<<l<<", mid="<<mid<<", r="<<r<<", s="<<s<<", h="<<h<<", i="<<i<<": "<<pre[i]<<" * "<<now<<endl;
        if (l <= h && h < mid) diff[h] += (s?+1:-1) * pre[i] * now;
      }
    }
    // mid <= h < r
    for (int s = 0; s < 2; ++s) {
      for (int i = mid; i >= l; --i) mxs[i] = mxss[0][i].first;
      for (int j = mid + 1; j <= r; ++j) mxs[j] = mxss[s][j].first;
      for (int j = mid + 1; j <= r; ++j) iss[j].clear();
      for (int i = l; i < mid; ++i) {
        on[i] = 0;
        if (i + mxs[i] <= r) iss[max(i + mxs[i], mid + 1)].push_back(i);
      }
      // valid: l <= i < k (<= mid)
      Mint now = 0;
      for (int k = l, j = mid + 1; j <= r; ++j) {
        for (const int i : iss[j]) {
          on[i] = 1;
          if (i < k) now += pre[i];
        }
        for (; k < mid && k <= j - mxs[j]; ++k) if (on[k]) now += pre[k];
        for (; k > l && !(k - 1 <= j - mxs[j]); --k) if (on[k - 1]) now -= pre[k - 1];
        const int h = mxss[0][j].second;
// if(mid<=h&&h<r)cerr<<"l="<<l<<", mid="<<mid<<", r="<<r<<", s="<<s<<", h="<<h<<", j="<<j<<": "<<now<<" * "<<suf[j]<<endl;
        if (mid <= h && h < r) diff[h] += (s?+1:-1) * now * suf[j];
      }
    }
    
    rec(mid, r);
  }
}
}  // hard


int main() {
  for (; ~scanf("%d", &N); ) {
    A.resize(N);
    for (int i = 0; i < N; ++i) {
      scanf("%d", &A[i]);
    }
    
    {
      using namespace easy;
      init();
      rec(0, N);
      pre = dp;
// cerr<<"pre = "<<pre<<endl;brute();
      reverse(A.begin(), A.end());
      init();
      rec(0, N);
      suf = dp;
      reverse(suf.begin(), suf.end());
// cerr<<"suf = "<<suf<<endl;brute();
      reverse(A.begin(), A.end());
    }
    {
      using namespace hard;
      init();
      rec(0, N);
// cerr<<"diff = "<<diff<<endl;
      for (int i = 0; i < N; ++i) {
        printf("%u\n", (pre[N] + diff[i]).x);
      }
// for(int i=0;i<N;++i){int a=1;swap(A[i],a);brute();swap(A[i],a);}
    }
  }
  return 0;
}