//floyd算法 
#include<stdio.h>
#include<limits.h>
int main(void)
{  
    int a, b, c, i, k, j, n, m, d[105][105];  
    while(scanf("%d%d", &n, &m), n!=0 || m!=0)
	{  
        for(i=1;i<=n;i++)
		{
			d[i][i] = 0;
			for(j=1;j<=i-1;j++)  
				d[i][j] = d[j][i] = INT_MAX;  
        }
		for(i=1;i<=m;i++)
		{  
			scanf("%d%d%d",&a,&b,&c);  
			d[a][b] = d[b][a] = c;   
		}   
        for(k=1;k<=n;k++)  
		{  
			for(i=1;i<=n;i++)
			{  
				for(j=1;j<=n;j++)
				{
					if(d[i][k]!=INT_MAX && d[k][j]!=INT_MAX && d[i][k]+d[k][j]<d[i][j])
						d[i][j] = d[i][k]+d[k][j];  
				}
			}  
		}
        printf("%d\n", d[1][n]);  
    }  
    return 0;  
}