#include<stdio.h>
int n,m,map[124][124];
int inf = 0x7fffffff;
void floyd( )
{
for( int i = 1; i <= n; ++i )
for( int j = 1; j <= n; ++j )
for( int k = 1; k <= n; ++k )
if( map[i][j] != inf && map[i][k] != inf )
if( map[i][j] + map[i][k] < map[j][k] )
map[j][k] = map[i][j] + map[i][k];
}
int main( )
{
while( scanf( "%d%d",&n,&m ),n&&m )
{
for( int i = 1; i <= n; ++i )
for( int j = 1; j <= n; ++j )
map[i][j] = inf;
for( int i = 1; i <= m; ++i )
{
int x,y,v;
scanf( "%d%d%d",&x,&y,&v );
if( map[x][y] > v )
map[x][y] = map[y][x] = v;
}
floyd( );
printf( "%d\n",map[1][n] );
}
return 0;
}
int n,m,map[124][124];
int inf = 0x7fffffff;
void floyd( )
{
for( int i = 1; i <= n; ++i )
for( int j = 1; j <= n; ++j )
for( int k = 1; k <= n; ++k )
if( map[i][j] != inf && map[i][k] != inf )
if( map[i][j] + map[i][k] < map[j][k] )
map[j][k] = map[i][j] + map[i][k];
}
int main( )
{
while( scanf( "%d%d",&n,&m ),n&&m )
{
for( int i = 1; i <= n; ++i )
for( int j = 1; j <= n; ++j )
map[i][j] = inf;
for( int i = 1; i <= m; ++i )
{
int x,y,v;
scanf( "%d%d%d",&x,&y,&v );
if( map[x][y] > v )
map[x][y] = map[y][x] = v;
}
floyd( );
printf( "%d\n",map[1][n] );
}
return 0;
}