C++ :

#include <bits/stdc++.h>
 
using namespace std;
const int maxn = 1e5 + 10;
const int inf = 0x3f3f3f3f;
 
struct node {
    int val, pos;
 
    bool operator<(const node &rhs) const {
        return val < rhs.val;
    }
};
 
set<node> p;
 
int main() {
    int n, a, b;
    scanf("%d", &n);
    scanf("%d", &a);
    p.insert({a, 1});
    set<node>::iterator q, t;
    for (int i = 2; i <= n; i++) {
        scanf("%d", &b);
        p.insert({b, i});
        if (p.size() == 2) {
            printf("%d 1\n", abs(a - b));
            continue;
        }
        q = p.find({b, i});
        if ((++q) == p.end()) {
            q--;
            node x = (*(--q));
            x.val = abs(b - x.val);
            printf("%d %d\n", x.val, x.pos);
            continue;
        } else if ((--q) == p.begin()) {
            node x;
            x.val = abs(b - (*(++q)).val);
            x.pos = (*(q)).pos;
            printf("%d %d\n", x.val, x.pos);
            continue;
        }
        node x, y;
        q--;
        x.val = (*(q)).val;
        x.pos = (*q).pos;
        q++;
        y.val = (*(++q)).val;
        y.pos = (*(q)).pos;
        if (abs(b - x.val) < abs(b - y.val))
            printf("%d %d\n", abs(b - x.val), x.pos);
        else if (abs(b - x.val) > abs(b - y.val))
            printf("%d %d\n", abs(b - y.val), y.pos);
        else {
            printf("%d %d\n", abs(b - y.val), x.pos);
        }
    }
    return 0;
}