Problem:
Score : 800 points

Problem Statement

There is a directed graph with N vertices and N edges. The vertices are numbered 1, 2, ..., N.

The graph has the following N edges: (p_1, 1), (p_2, 2), ..., (p_N, N), and the graph is weakly connected. Here, an edge from Vertex u to Vertex v is denoted by (u, v), and a weakly connected graph is a graph which would be connected if each edge was bidirectional.

We would like to assign a value to each of the vertices in this graph so that the following conditions are satisfied. Here, a_i is the value assigned to Vertex i.

Each a_i is a non-negative integer.

For each edge (i, j), a_i \neq a_j holds.

For each i and each integer x(0 ≤ x < a_i), there exists a vertex j such that the edge (i, j) exists and x = a_j holds.

Determine whether there exists such an assignment.

Constraints

2 ≤ N ≤ 200 000

1 ≤ p_i ≤ N

p_i \neq i

The graph is weakly connected.

Input

Input is given from Standard Input in the following format:

N
p_1 p_2 ... p_N

Output

If the assignment is possible, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

4
2 3 4 1

Sample Output 1

POSSIBLE

The assignment is possible: {a_i} = {0, 1, 0, 1} or {a_i} = {1, 0, 1, 0}.

Sample Input 2

3
2 3 1

Sample Output 2

IMPOSSIBLE

Sample Input 3

4
2 3 1 1

Sample Output 3

POSSIBLE

The assignment is possible: {a_i} = {2, 0, 1, 0}.

Sample Input 4

6
4 5 6 5 6 4

Sample Output 4

IMPOSSIBLE

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

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

#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
//const ll mod = 1000000007;
bool visited[200050];
int parent[200050];
vector<int> children[200050];
int Grundy[200050];
bool test_visited[200050][2];
int test_Grundy[200050][2];

void bfs(int from) {
    if(visited[from]) return;
    for(int i = 0; i < children[from].size(); i++) {
        int to = children[from][i];
        if(!visited[to]) return;
    }
    vector<int> now;
    now.push_back(10000000);
    for(int i = 0; i < children[from].size(); i++) {
        int to = children[from][i];
        now.push_back(Grundy[to]);
    }
    sort(now.begin(), now.end());
    now.erase(unique(now.begin(), now.end()), now.end());
    for(int i = 0; i < now.size(); i++){
        if(now[i] != i) {
            Grundy[from] = i;
            break;
        }
    }
    visited[from] = true;
    bfs(parent[from]);
    return;
}

void test_bfs(int from, int index) {
    if(test_visited[from][index]) return;
    //cout << "visiting " << from << endl;
    for(int i = 0; i < children[from].size(); i++) {
        int to = children[from][i];
        if(!test_visited[to][index]) return;
    }
    vector<int> now;
    now.push_back(10000000);
    for(int i = 0; i < children[from].size(); i++) {
        int to = children[from][i];
        now.push_back(test_Grundy[to][index]);
    }
    sort(now.begin(), now.end());
    now.erase(unique(now.begin(), now.end()), now.end());
    for(int i = 0; i < now.size(); i++){
        if(now[i] != i) {
            test_Grundy[from][index] = i;
            break;
        }
    }
    test_visited[from][index] = true;
    test_bfs(parent[from], index);
    return;
}

int main() {
    //cout.precision(10)
    int N;
    cin >> N;
    for(int i = 1; i <= N; i++) {
        Grundy[i] = -1;
        int p;
        cin >> p;
        parent[i] = p;
        children[p].push_back(i);
    }
    bool is_loop = true;
    for(int i = 1; i <= N; i++) {
        if(children[i].empty()) is_loop = false;
    }
    if(is_loop) {
        if(N % 2 == 0) cout << "POSSIBLE" << endl;
        else cout << "IMPOSSIBLE" << endl;
        return 0;
    }
    for(int i = 1; i <= N; i++) {
        bfs(i);
    }
    for(int i = 1; i <= N; i++) {
        //cout << i << " " << Grundy[i] << endl;
    }
    int test_point = 1;
    for(int i = 1; i <= N; i++) {
        for(int j = 0; j < 2; j++) {
            test_visited[i][j] = visited[i];
            test_Grundy[i][j] = Grundy[i];
        }
        if(!visited[i]) test_point = i;
    }
    vector<int> now;
    now.push_back(1000000);
    for(int i = 0; i < children[test_point].size(); i++) {
        int to = children[test_point][i];
        if(Grundy[to] != -1) now.push_back(Grundy[to]);
    }
    sort(now.begin(), now.end());
    now.erase(unique(now.begin(), now.end()), now.end());
    for(int i = 0; i < now.size(); i++) {
        if(now[i] != i) {
            test_Grundy[test_point][0] = i;
            test_Grundy[test_point][1] = i + 1;
            //cout << test_point << " " << i << endl;
            break;
        }
    }
    test_visited[test_point][0] = true;
    test_visited[test_point][1] = true;
    test_bfs(parent[test_point], 0);
    test_bfs(parent[test_point], 1);
    for(int i = 1; i <= N; i++) {
        //cout << i << " " << test_Grundy[i][1] << endl;
    }
    for(int j = 0; j <= 1; j++) {
        vector<int> now;
        now.push_back(1000000);
        for(int i = 0; i < children[test_point].size(); i++) {
            int to = children[test_point][i];
            now.push_back(test_Grundy[to][j]);
        }
        sort(now.begin(), now.end());
        now.erase(unique(now.begin(), now.end()), now.end());
        for(int i = 0; i < now.size(); i++) {
            //cout << j << " " << i << now[i] << endl;
            if(i != now[i]) {
                if(test_Grundy[test_point][j] == i) {
                    //cout << i << endl;
                    //cout << j << endl;
                    //cout << test_point << endl;
                    cout << "POSSIBLE" << endl;
                    return 0;
                }
                break;
            }
        }
    }
    cout << "IMPOSSIBLE" << endl;
    return 0;
}