#include<bits/stdc++.h>
using namespace std;

//#define int long long
using ll = long long;
const int N = 5e3 + 10;
const ll mod = 998244353;

int n;
ll dp[N], g[N][N], mul[N];
int p[N], sz[N];
vector<int> t[N];

ll f[N], invf[N], inv[N];

ll qpow (ll x, ll k) {
    ll res = 1;
    while (k) {
        if (k & 1) res = res * x % mod;
        x = x * x % mod;
        k >>= 1;
    }
    return res;
}
ll getinv (ll x) {
    return qpow(x, mod - 2);
}

void init () {
    cin >> n;
    for (int i = 2; i <= n; i ++) {
        cin >> p[i];
        t[p[i]].push_back(i);
    }

    inv[0] = invf[0] = f[0] = 1;
    for (int i = 1; i <= n; i ++) {
        f[i] = f[i - 1] * i % mod;
        inv[i] = getinv(i);
        invf[i] = invf[i - 1] * inv[i] % mod;
    }
}

ll dp_sum[N], dp_inv[N];

void dfs0 (int x) {
    sz[x] = 1;
    mul[x] = 1;
    dp_sum[x] = 1;
    for (auto y: t[x]) {
        dfs0(y);
        dp_sum[x] = dp_sum[x] * dp[y] % mod;
        sz[x] += sz[y];
        mul[x] = mul[x] * invf[sz[y]] % mod;
    }
    dp[x] = f[sz[x] - 1] * mul[x] % mod * dp_sum[x] % mod;
    dp_inv[x] = getinv(dp[x]);
}

ll pre[N][N];

ll getC (int x, int y) {
    return f[x] * invf[y] % mod * invf[x - y] % mod;
}

void dfs (int x) {
    if (x > 1) {
        for (int i = 1; i <= n; i ++) {
            g[x][i] = pre[p[x]][i - 1] * getC(n - i, sz[x] - 1) % mod;
//          g[x][i] = g[x][i] * f[sz[p[x]] - 1 - sz[x]] % mod * mul[p[x]] % mod * f[sz[x]] % mod;
//          g[x][i] = g[x][i] * dp_sum[p[x]] % mod * dp_inv[x] % mod;
        }
    }
    for (int i = 1; i <= n; i ++) {
        pre[x][i] = (pre[x][i - 1] + g[x][i]) % mod;
    }
    for (auto y: t[x]) {
        dfs(y);
    }
}

void solve () {
    init();
    dfs0(1);

//  for (int i = 1; i <= n; i ++) {
//      cout << i << " : " << dp[i] << endl;
//  }

    g[1][1] = 1;
    dfs(1);
    for (int i = 1; i <= n; i ++) {
        cout << i << " : ";
        for (int j = 1; j <= n; j ++) {
            cout << g[i][j] << " \n"[j == n];
        }
    }

    for (int i = 1; i <= n; i ++) {
        cout << g[i][i] * dp[i] % mod << " \n"[i == n];
    }
}

signed main () {
    ios::sync_with_stdio(0);
    cin.tie(0);

    int _ = 1;
//  cin >> _;
    while (_ --) {
        solve();
    }

    return 0;
}