Problem:
Score : 400 points

Problem Statement

One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

Constraints

1 ≦ N ≦ 200,000

(a_1, a_2, ..., a_N) is a permutation of (1, 2, ..., N).

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the answer.

Note that the answer may not fit into a 32-bit integer.

Sample Input 1

3
2 1 3

Sample Output 1

9

Sample Input 2

4
1 3 2 4

Sample Output 2

19

Sample Input 3

8
5 4 8 1 2 6 7 3

Sample Output 3

85

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
	MyScanner sc = new MyScanner();
	Scanner sc2 = new Scanner(System.in);
	long start = System.currentTimeMillis();
	long fin = System.currentTimeMillis();
	final int MOD = 1000000007;
	int[] dx = { 1, 0, 0, -1 };
	int[] dy = { 0, 1, -1, 0 };

	void run() {
		int N = sc.nextInt();
		int[] a = sc.nextIntArray(N);
		Pair[] p = new Pair[N];
		for (int i = 0; i < N; i++) {
			p[i] = new Pair(a[i], i);
		}
		Arrays.sort(p);
		long cnt = 0;

		UnionFind uf = new UnionFind();
		uf.init(N);

		for (int i = 0; i < N; i++) {
			long g1 = 1;
			long g2 = 1;
			if(p[i].pos + 1 < N  && p[i].num < a[p[i].pos + 1]) {
				g1 += uf.getGroupSize(p[i].pos + 1);
				uf.union(p[i].pos, p[i].pos + 1);
			}
			if(p[i].pos - 1 >= 0 && p[i].num < a[p[i].pos - 1]) {
				g2 += uf.getGroupSize(p[i].pos - 1);
				uf.union(p[i].pos, p[i].pos - 1);
			}
			cnt += p[i].num * ( g1 * g2);
		}

		System.out.println(cnt);
	}

	class Pair implements Comparable<Pair> {

		int num;
		int pos;

		public Pair() {
			super();
			this.num = 0;
			this.pos = 0;
		}

		public Pair(int num, int pos) {
			super();
			this.num = num;
			this.pos = pos;
		}

		@Override
		public int compareTo(Pair arg0) {
			return -(this.num - arg0.num);
		}

		void show() {
			System.out.println("num = " + this.num + " pos = " + this.pos);
		}
	}

	public class UnionFind {

		int[] par;
		int[] rank;
		int groupCnt;

		void init(int n) {
			groupCnt = n;
			par = new int[n];
			rank = new int[n];
			Arrays.fill(par, -1);
		}

		void union(int x, int y) {
			x = find(x);
			y = find(y);
			if (x == y) {
				return;
			}
			groupCnt--;
			if (rank[x] < rank[y]) {
				par[y] += par[x];
				par[x] = y;
			} else {
				par[x] += par[y];
				par[y] = x;
				if (rank[x] == rank[y]) {
					rank[x]++;
				}
			}
		}

		int find(int x) {
			if (par[x] < 0) {
				return x;
			} else {
				return par[x] = find(par[x]);
			}
		}

		boolean same(int x, int y) {
			return find(x) == find(y);
		}

		int getGroupSize(int x) {
			return -par[find(x)];
		}

		int getGroupCnt() {
			return groupCnt;
		}
	}

	public static void main(String[] args) {
		new Main().run();
	}

	void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	void debug2(char[][] array) {
		for (int i = 0; i < array.length; i++) {
			for (int j = 0; j < array[i].length; j++) {
				System.out.print(array[i][j]);
			}
			System.out.println();
		}
	}

	boolean inner(int h, int w, int limH, int limW) {
		return 0 <= h && h < limH && 0 <= w && w < limW;
	}

	void swap(int[] x, int a, int b) {
		int tmp = x[a];
		x[a] = x[b];
		x[b] = tmp;
	}

	// find minimum i (k <= a[i])
	int lower_bound(int a[], int k) {
		int l = -1;
		int r = a.length;
		while (r - l > 1) {
			int mid = (l + r) / 2;
			if (k <= a[mid])
				r = mid;
			else
				l = mid;
		}
		// r = l + 1
		return r;
	}

	// find minimum i (k < a[i])
	int upper_bound(int a[], int k) {
		int l = -1;
		int r = a.length;
		while (r - l > 1) {
			int mid = (l + r) / 2;
			if (k < a[mid])
				r = mid;
			else
				l = mid;
		}
		// r = l + 1
		return r;
	}

	long gcd(long a, long b) {
		return a % b == 0 ? b : gcd(b, a % b);
	}

	long lcm(long a, long b) {
		return a * b / gcd(a, b);
	}

	boolean palindrome(String s) {
		for (int i = 0; i < s.length() / 2; i++) {
			if (s.charAt(i) != s.charAt(s.length() - 1 - i)) {
				return false;
			}
		}
		return true;
	}

	class MyScanner {
		int nextInt() {
			try {
				int c = System.in.read();
				while (c != '-' && (c < '0' || '9' < c))
					c = System.in.read();
				if (c == '-')
					return -nextInt();
				int res = 0;
				do {
					res *= 10;
					res += c - '0';
					c = System.in.read();
				} while ('0' <= c && c <= '9');
				return res;
			} catch (Exception e) {
				return -1;
			}
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		String next() {
			try {
				StringBuilder res = new StringBuilder("");
				int c = System.in.read();
				while (Character.isWhitespace(c))
					c = System.in.read();
				do {
					res.append((char) c);
				} while (!Character.isWhitespace(c = System.in.read()));
				return res.toString();
			} catch (Exception e) {
				return null;
			}
		}

		int[] nextIntArray(int n) {
			int[] in = new int[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextInt();
			}
			return in;
		}

		int[][] nextInt2dArray(int n, int m) {
			int[][] in = new int[n][m];
			for (int i = 0; i < n; i++) {
				in[i] = nextIntArray(m);
			}
			return in;
		}

		double[] nextDoubleArray(int n) {
			double[] in = new double[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextDouble();
			}
			return in;
		}

		long[] nextLongArray(int n) {
			long[] in = new long[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextLong();
			}
			return in;
		}

		char[][] nextCharField(int n, int m) {
			char[][] in = new char[n][m];
			for (int i = 0; i < n; i++) {
				String s = sc.next();
				for (int j = 0; j < m; j++) {
					in[i][j] = s.charAt(j);
				}
			}
			return in;
		}
	}
}