Problem:
Score : 300 points

Problem Statement

There are N observatories in AtCoder Hill, called Obs. 1, Obs. 2, ..., Obs. N. The elevation of Obs. i is H_i.
There are also M roads, each connecting two different observatories. Road j connects Obs. A_j and Obs. B_j.

Obs. i is said to be good when its elevation is higher than those of all observatories that can be reached from Obs. i using just one road.
Note that Obs. i is also good when no observatory can be reached from Obs. i using just one road.

How many good observatories are there?

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq H_i \leq 10^9

1 \leq A_i,B_i \leq N

A_i \neq B_i

Multiple roads may connect the same pair of observatories.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
H_1 H_2 ... H_N
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Print the number of good observatories.

Sample Input 1

4 3
1 2 3 4
1 3
2 3
2 4

Sample Output 1

2

From Obs. 1, you can reach Obs. 3 using just one road. The elevation of Obs. 1 is not higher than that of Obs. 3, so Obs. 1 is not good.

From Obs. 2, you can reach Obs. 3 and 4 using just one road. The elevation of Obs. 2 is not higher than that of Obs. 3, so Obs. 2 is not good.

From Obs. 3, you can reach Obs. 1 and 2 using just one road. The elevation of Obs. 3 is higher than those of Obs. 1 and 2, so Obs. 3 is good.

From Obs. 4, you can reach Obs. 2 using just one road. The elevation of Obs. 4 is higher than that of Obs. 2, so Obs. 4 is good.

Thus, the good observatories are Obs. 3 and 4, so there are two good observatories.

Sample Input 2

6 5
8 6 9 1 2 1
1 3
4 2
4 3
4 6
4 6

Sample Output 2

3

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

function Main(_input) {
    var input = _input.split("\n");
    var firstLine = input[0].split(" ");
    var secondLine = input[1].split(" ");
    var num_N = parseInt(firstLine[0]);
    var num_M = parseInt(firstLine[1]);
    var arr_Height = new Array();
    var arr_Road = new Array();
    var ans = 0;
    for( var i = 0; i < num_N ; i++) { arr_Height.push(parseInt(secondLine[i])); }
    for( var j = 0; j < num_M; j++ ) { arr_Road.push(input[j + 2].split(" ")); }

    for( var m = 0; m < num_N; m++ ){
        var result = true;
        var heightOfTower = arr_Height[m];
        var numTower = m+1;
        for( var h = 0; h < num_M; h++ ){
            var singleRoad = arr_Road[h];
            if( parseInt(singleRoad[0]) == numTower || parseInt(singleRoad[1]) == numTower  ){
                var rivalHeight = singleRoad[0] == numTower ? arr_Height[ parseInt(singleRoad[1]) - 1 ] : arr_Height[ parseInt(singleRoad[0]) - 1 ];
                if( rivalHeight >= heightOfTower ){
                    result = false;
                    break;
                } 
            }
        }
        if(result) ans++;
    }

    console.log(ans);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));