function processData(input) {
    var temp = input.split('\n')
    var [ N, I ] = temp.shift().split(' ').map( Number )

    // generate graph
    var graph = [] // store in an array of Set [ 0 : [ 0, 1 ], 1 : [ 3, 2 ] ] (to prevent duplicate)
    var relationalMap = {} // use to remember the map { 0 : 0, 1 : 0, 2 : 1, 3 : 1 }

    for(let i = 0; i < I;i++)
    {
        var [ ast1, ast2 ] = temp.shift().split(' ').map( Number )

        // if both of the ast1 and ast2 found in the different map => group two map
        if ( relationalMap.hasOwnProperty( ast1 ) && relationalMap.hasOwnProperty( ast2 ) )
        {
	    // console.log('[both found]', ast1, ast2, relationalMap)
            var graphIndex = relationalMap[ ast1 ]
            var graphIndex2 = relationalMap[ ast2 ]

            // continue if there are already in the graph
            if ( graphIndex === graphIndex2 ) continue
            // update the set from 2 to 1, and clear set 2
            for( let i of graph[ graphIndex2 ] )
            {
                graph[ graphIndex ].add( i )
                relationalMap[ i ] = graphIndex
            }
            graph[ graphIndex2 ].clear()
        }
        // if one of ast1 and ast2 found in the map
        else if ( relationalMap.hasOwnProperty( ast1 ) || relationalMap.hasOwnProperty( ast2 ) )
        {
	    // console.log('[one found]', ast1, ast2, relationalMap)
            let graphIndex = relationalMap[ ast1 ] || relationalMap[ ast2 ]
            graph[ graphIndex ].add( ast1 ).add( ast2 )
            relationalMap[ ast1 ] = graphIndex
            relationalMap[ ast2 ] = graphIndex
        }
	// if ast1 ast2 not found in the map
        else if ( !relationalMap.hasOwnProperty( ast1 ) && !relationalMap.hasOwnProperty( ast2 ) )
        {
	    // console.log('[not found]', ast1, ast2, relationalMap)
            let graphSet = new Set()
            graphSet.add( ast1 ).add( ast2 )
            let graphIndex = ( graph.push( graphSet ) - 1 ) + ''
            relationalMap[ ast1 ] = graphIndex
            relationalMap[ ast2 ] = graphIndex
        }
    }
    // console.log('[graph]', graph);
    // console.log('[relationalMap]', relationalMap)

    // denotes the number of permissible ways to choose a pair of astronauts.
    var ways = 0;
    for( let i = 0;i < graph.length - 1; i++)
    {
        let waysi = graph[i].size
        for( let j = i + 1; j < graph.length; j++ )
        {
            let waysj = graph[j].size
            ways += waysi * waysj
        }
    }

    // and those who is alone in their country
    let alone = N - Object.keys( relationalMap ).length
    ways += Object.keys(relationalMap).length * ( N - Object.keys(relationalMap).length )
    ways += c(alone, 2)

    console.log(ways)
}

function c(n, x)
{
    let numerator = n
    for(let i = n-1;i>(n-x);i--)
    {
        numerator *= i
    }

    let denominator = x
    for(let i = x - 1 ;i>=2;i--)
    {
        denominator *= i
    }

    return numerator/denominator
}