#include <bits/stdc++.h>
using namespace std;
#define ull unsigned __int128
ull C[405][405];

ull calc(int x, int y) {
	return C[x + y][x] - C[x + y][x + 1];
}
int fl = 0;
vector<int> g[405];
ull ret;
int x, y;

void dfs(int u) {
	if (u > 1) {
		ret += calc(x - 1, y);
		y--;
	}
	for (int v : g[u]) {
		dfs(v);
	}
	if (u > 1) {
		x--;
	}
}

ull encoder(int n, const int *p) {
	for (int i = 1; i <= n; i++) {
		g[i].clear();
	}
	ret = 0;
	if (!fl) {
		C[0][0] = 1;
		for (int i = 1; i <= 150; i++) {
			C[i][0] = 1;
			C[i][i] = 1;
			for (int j = 1; j < i; j++) {
				C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
			}
		}
		fl = 1;
	}
	for (int i = 2; i <= n; i++) {
		g[p[i]].push_back(i);
	}
	x = y = n - 1;
	dfs(1);
	return ret;
}
int tot = 0;
int st[405], a[405], top;

void decoder(int n, ull X, int *p) {
	tot = 1;
	if (!fl) {
		C[0][0] = 1;
		for (int i = 1; i <= 150; i++) {
			C[i][0] = 1;
			C[i][i] = 1;
			for (int j = 1; j < i; j++) {
				C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
			}
		}
		fl = 1;
	}
	int x = n - 1, y = n - 1;
	for (int i = 1; i <= 2 * n - 2; i++) {
		if (X >= calc(x - 1, y)) {
			X -= calc(x - 1, y);
			a[i] = 1;
			y--;
		} else {
			x--;
			a[i] = 0;
		}
	}
	p[1] = 0;
	st[1] = 1;
	tot = top = 1;
	for (int i = 1; i <= 2 * n - 2; i++) {
		if (a[i]) {
			tot++;
			p[tot] = st[top];
			top++;
			st[top] = tot;
		} else {
			top--;
		}
	}
}