This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
int max(int x,int y)
{
if(x>y) return x;
return y;
}
int min(int x,int y)
{
if(x>y) return y;
return x;
}
int n;
int p,t=1,a[600010],ch[600010],top,q[2500010],s[600010],e[600010],dap[600010],f,r,treeb[2500010],treef[2500010],tree[2500010];
int top2;
struct data
{
int k,x,y,sw;
}arr[100];
void update(int x,int gap)
{
int s=x+t-1;
tree[s]=gap;
s/=2;
while(s>0){
tree[s]=max(tree[s*2],tree[s*2+1]);
s/=2;
}
}
void updatef(int x,int gap)
{
int s=x+t-1;
treef[s]=gap;
s/=2;
while(s>0){
treef[s]=min(treef[s*2],treef[s*2+1]);
s/=2;
}
}
void updateb(int x,int gap)
{
int s=x+t-1;
treeb[s]=gap;
s/=2;
while(s>0){
treeb[s]=max(treeb[s*2],treeb[s*2+1]);
s/=2;
}
}
int queryf(int x,int y,int k,int s,int e)
{
top2=0;
if(s>e) return 2147483647;
int mini=2147483647;
top2++; arr[top2].x=x; arr[top2].y=y; arr[top2].k=k; arr[top2].sw=0;
while(top2>0)
{
x=arr[top2].x; y=arr[top2].y; k=arr[top2].k;
if(s<=x && y<=e){mini=min(treef[k],mini), top2--; continue;}
if(s>y || e<x){top2--; continue;}
if(arr[top2].sw==0)
{
arr[top2].sw=1;
top2++; arr[top2].x=x; arr[top2].y=(x+y)/2; arr[top2].k=k*2; arr[top2].sw=0;
}
else if(arr[top2].sw==1)
{
arr[top2].sw=2;
top2++; arr[top2].x=(x+y)/2+1; arr[top2].y=y; arr[top2].k=k*2+1; arr[top2].sw=0;
}
else top2--;
}
return mini;
}
int queryb(int x,int y,int k,int s,int e)
{
top2=0;
if(s>e) return 0;
int maxi=0;
top2++; arr[top2].x=x; arr[top2].y=y; arr[top2].k=k; arr[top2].sw=0;
while(top2>0)
{
x=arr[top2].x; y=arr[top2].y; k=arr[top2].k;
if(s<=x && y<=e){maxi=max(treeb[k],maxi), top2--; continue;}
if(s>y || e<x){top2--; continue;}
if(arr[top2].sw==0)
{
arr[top2].sw=1;
top2++; arr[top2].x=x; arr[top2].y=(x+y)/2; arr[top2].k=k*2; arr[top2].sw=0;
}
else if(arr[top2].sw==1)
{
arr[top2].sw=2;
top2++; arr[top2].x=(x+y)/2+1; arr[top2].y=y; arr[top2].k=k*2+1; arr[top2].sw=0;
}
else top2--;
}
return maxi;
}
int query(int x,int y,int k,int s,int e)
{
top2=0;
if(s>e) return 0;
int maxi=0;
top2++; arr[top2].x=x; arr[top2].y=y; arr[top2].k=k; arr[top2].sw=0;
while(top2>0)
{
x=arr[top2].x; y=arr[top2].y; k=arr[top2].k;
if(s<=x && y<=e){maxi=max(tree[k],maxi), top2--; continue;}
if(s>y || e<x){top2--; continue;}
if(arr[top2].sw==0)
{
arr[top2].sw=1;
top2++; arr[top2].x=x; arr[top2].y=(x+y)/2; arr[top2].k=k*2; arr[top2].sw=0;
}
else if(arr[top2].sw==1)
{
arr[top2].sw=2;
top2++; arr[top2].x=(x+y)/2+1; arr[top2].y=y; arr[top2].k=k*2+1; arr[top2].sw=0;
}
else top2--;
}
return maxi;
}
void check()
{
int i;
//1
for(i=1;i<=n;i++){
if(dap[i]==1) update(s[i],e[i]);
}
for(i=1;i<=n;i++){
if(dap[i]==1 && query(1,t,1,s[i]+1,e[i]-1)>e[i]){printf("IMPOSSIBLE"); exit(0);}
}
memset(tree,0,sizeof tree);
//0
for(i=1;i<=n;i++){
if(dap[i]==0) update(s[i],e[i]);
}
for(i=1;i<=n;i++){
if(dap[i]==0 && query(1,t,1,s[i]+1,e[i]-1)>e[i]){printf("IMPOSSIBLE"); exit(0);}
}
}
int main()
{
int i;
scanf("%d",&n);
for(i=1;i<=n*2;i++)
{
scanf("%d",&a[i]);
if(s[a[i]]==0) s[a[i]]=i;
else e[a[i]]=i;
}
for(i=1;;i++){if(t>=n*2) break; t*=2;}
for(i=1;i<=t*2;i++) treef[i]=2147483647;
for(i=1;i<=n;i++)
{
updatef(e[i],s[i]);
updateb(s[i],e[i]);
}
for(i=1;i<=n;i++)
{
if(ch[i]==0)
{
ch[i]=1;
dap[i]=1;
q[++r]=i;
updatef(e[i],2147483647);
updateb(s[i],0);
while(f!=r)
{
f++;
for(;;)
{
p=queryf(1,t,1,s[q[f]]+1,e[q[f]]-1);
if(p>=s[q[f]]) break;
updatef(e[a[p]],2147483647);
dap[a[p]]=(dap[q[f]]+1)%2;
ch[a[p]]=1;
q[++r]=a[p];
}
for(;;)
{
p=queryb(1,t,1,s[q[f]]+1,e[q[f]]-1);
if(p<=e[q[f]]) break;
updateb(s[a[p]],0);
dap[a[p]]=(dap[q[f]]+1)%2;
ch[a[p]]=1;
q[++r]=a[p];
}
}
}
}
check();
for(i=1;i<=n*2;i++)
{
if(dap[a[i]]==0) printf("v");
else printf("^");
}
return 0;
}
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