#include<bits/stdc++.h>
using namespace std;
const int N = 5005, mod = 998244353;
int fa[N], siz[N], prod[N], invp[N], fac[N], inv[N];
int g[N][N], dep[N], n, pre[N];
vector <int> E[N];
int power(int a, int b) {
    int res = 1;
    while (b) {
        if (b & 1) res = 1ll * res * a % mod;
        a = 1ll * a * a % mod, b >>= 1;
    }
    return res;
}
int C(int n, int m) {
    return 1ll * fac[n] * inv[m] % mod * inv[n - m] % mod;
}
void dfs(int u) {
    siz[u] = prod[u] = 1;
    dep[u] = dep[fa[u]] + 1;
    for (int v : E[u]) {
        dfs(v);
        siz[u] += siz[v];
        prod[u] = 1ll * prod[u] * prod[v] % mod;
    }
    prod[u] = 1ll * prod[u] * siz[u] % mod;
    invp[u] = power(prod[u], mod - 2);
}
void dp(int u) {
    pre[dep[u] - 1] = 0;
    for (int v : E[u]) {
        int tmp = 1ll * fac[siz[u] - siz[v]] % mod * invp[u] % mod * prod[v] % mod * siz[u] % mod * power(siz[u] - siz[v], mod - 2) % mod;
        for (int x = dep[u]; x <= n - siz[u] + 1; ++x) {
            // if (!g[u][x]) continue;
            pre[x] = (pre[x - 1] + 1ll * C(n - siz[v] - x, siz[u] - siz[v] - 1) * tmp % mod * g[u][x]) % mod;
        }
        for (int x = n - siz[u] + 2; x <= n - siz[v] + 1; ++x) pre[x] = pre[x - 1];
        for (int y = dep[v]; y <= n - siz[v] + 1; ++y) {
            g[v][y] = pre[y - 1];
        }
        dp(v);
    }
}
int main() {
    cin.tie(nullptr) -> ios::sync_with_stdio(false);
    cout.tie(0);
    cin >> n;
    for (int i = 2; i <= n; ++i) {
        cin >> fa[i];
        E[fa[i]].push_back(i);
    }
    fac[0] = 1;
    for (int i = 1; i <= n; ++i)
        fac[i] = 1ll * fac[i - 1] * i % mod;
    inv[n] = power(fac[n], mod - 2);
    for (int i = n; i >= 1; --i)
        inv[i - 1] = 1ll * inv[i] * i % mod;
    dfs(1);
    g[1][1] = 1;
    dp(1);
    // for (int i = 1; i <= n; ++i)
    //     for (int j = dep[i]; j <= n - siz[i] + 1; ++j)
    //         printf("g[%d][%d] = %d\n", i, j, g[i][j]);
    for (int i = 1; i <= n; ++i) {
        int res = 1ll * g[i][i] * C(n - i, siz[i] - 1) % mod * fac[siz[i]] % mod * invp[i] % mod;
        cout << res << endl;
    }
    return 0;
}
/*
4
1 1 2
9
1 1 2 2 3 3 4 5
*/