3883 | 3885 | 3882 | 3880 | 3881 | 3878 | 3877 | 3876 | 3871 | 3872 | 3874 | 3869 | 3870 | 3866 | 3867 | 3864 | 3863 | 3862 | 3861 | 3860 | 3859 | 3838 | 3857 | 3858 | 3855 | 3856 | 3851 | 3853 | 3854 | 3849 | 3850 | 3852 | 3846 | 3848 | 3843 | 3840 | 3841 | 3842 | 3837 | 3836 | 3833 | 3831 | 3832 | 3829 | 3827 | 3828 | 3826 | 3824 | 3823 | 3822 | 3820 | 3819 | 3818 | 3815 | 3816 | 3817 | 3814 | 3813 | 3811 | 3810 | 3806 | 3807 | 3808 | 3805 | 3803 | 3802 | 3801 | 3800 | 3797 | 3798 | 3796 | 3793 | 3794 | 3792 | 3789 | 3786 | 3784 | 3787 | 3781 | 3779 | 3775 | 3773 | 3774 | 3772 | 3767 | 3768 | 3769 | 3762 | 3760 | 3759 | 3755 | 3752 | 3753 | 3754 | 3750 | 3748 | 3749 | 3742 | 3743 | 3745 | 3746 | 3747 | 3740 | 3737 | 3738 | 3739 | 3736 | 3734 | 3733 | 3732 | 3731 | 3729 | 3728 | 3726 | 3725 | 3724 | 3723 | 3721 | 3719 | 3720 | 3718 | 3716 | 3713 | 3712 | 3711 | 3710 | 3709 | 3707 | 3708 | 3706 | 3705 | 3704 | 3702 | 3701 | 3700 | 3699 | 3698 | 3695 | 3696 | 3697 | 3692 | 3693 | 3694 | 3690 | 3691 | 3689 | 3688 | 3685 | 3686 | 3679 | 3678 | 3676 | 3675 | 3674 | 3672 | 3673 | 3663 | 3664 | 3661 | 3656 | 3657 | 3658 | 3659 | 3651 | 3652 | 3654 | 3655 | 3650 | 3649 | 3648 | 3646 | 3647 | 3644 | 3645 | 3643 | 3642 | 3640 | 3639 | 3637 | 3636 | 3634 | 3635 | 3632 | 3631 | 3629 | 3630 | 3626 | 3627 | 3624 | 3625 | 3622 | 3623 | 3620 | 3619 | 3612 | 3610 | 3611 | 3606 | 3607 | 3608 | 3609 | 3602 | 3603 | 3604 | 3605 | 3601 | 3600 | 3599 | 3598 | 3596 | 3595 | 3594 | 3593 | 3591 | 3592 | 3588 | 3589 | 3585 | 3586 | 3584 | 3580 | 3581 | 3582 | 3583 | 3579 | 3577 | 3578 | 3576 | 3574 | 3572 | 3573 | 3571 | 3569 | 3570 | 3568 | 3567 | 3565 | 3562 | 3563 | 3560 | 3561 | 3559 | 3557 | 3556 | 3555 | 3554 | 3553 | 3551 | 3552 | 3550 | 3549 | 3548 | 3547 | 3546 | 3544 | 3545 | 3543 | 3542 | 3538 | 3539 | 3540 | 3541 | 3536 | 3537 | 3535 | 3534 | 3531 | 3532 | 3533 | 3529 | 3530 | 3527 | 3528 | 3526 | 3525 | 3524 | 3523 | 3522 | 3520 | 3518 | 3516 | 3517 | 3515 | 3514 | 3512 | 3513 | 3511 | 3510 | 3509 | 3508 | 3507 | 3506 | 3505 | 3504 | 3046 | 3503 | 3493 | 3494 | 3490 | 3491 | 3486 | 3489 | 3485 | 3481 | 3483 | 3492 | 3479 | 3480 | 3476 | 3477 | 3474 | 3473 | 3471 | 3470 | 3469 | 3468 | 3465 | 3466 | 3467 | 3463 | 3459 | 3460 | 3461 | 3462 | 3458 | 3457 | 3456 | 3455 | 3454 | 3452 | 3449 | 3448 | 3447 | 3446 | 3445 | 3443 | 3444 | 3442 | 3441 | 3439 | 3440 | 3437 | 3438 | 3435 | 3436 | 3431 | 3433 | 3434 | 3430 | 3427 | 3428 | 3425 | 3426 | 3423 | 3422 | 3419 | 3421 | 3418 | 3415 | 3416 | 3417 | 3414 | 3413 | 3411 | 3412 | 3409 | 3410 | 3408 | 3401 | 3402 | 3403 | 3404 | 3406 | 3407 | 3400 | 3399 | 3397 | 3393 | 3394 | 3396 | 3392 | 3391 | 3387 | 3389 | 3390 | 3385 | 3384 | 3383 | 3382 | 3379 | 3380 | 3381 | 3378 | 3376 | 3375 | 3374 | 3373 | 3372 | 3370 | 3367 | 3368 | 3369 | 3364 | 3363 | 3360 | 3359 | 3358 | 3356 | 3355 | 3354 | 3352 | 3349 | 3348 | 3347 | 3344 | 3345 | 3346 | 3343 | 3342 | 3340 | 3338 | 3339 | 3337 | 3335 | 3336 | 3334 | 3333 | 3330 | 3322 | 3319 | 3320 | 3321 | 3317 | 3316 | 3313 | 3314 | 3315 | 3312 | 3310 | 3311 | 3309 | 3307 | 3308 | 3306 | 3304 | 3303 | 3302 | 3300 | 3301 | 3298 | 3299 | 3296 | 3295 | 3293 | 3294 | 3292 | 3291 | 3290 | 3289 | 3288 | 3286 | 3285 | 3284 | 3280 | 3281 | 3282 | 3278 | 3277 | 3272 | 3273 | 3274 | 3275 | 3276 | 3271 | 3270 | 3267 | 3268 | 3265 | 3266 | 3264 | 3262 | 3261 | 3260 | 3259 | 3258 | 3257 | 3256 | 3255 | 3253 | 3254 | 3251 | 3248 | 3247 | 3245 | 3246 | 3244 | 3241 | 3239 | 3236 | 3237 | 3235 | 3234 | 3233 | 3231 | 3232 | 3230 | 3229 | 3201 | 3202 | 3203 | 3204 | 3205 | 3206 | 3207 | 3208 | 3209 | 3210 | 3211 | 3212 | 3213 | 3214 | 3215 | 3216 | 3217 | 3219 | 3220 | 3222 | 3223 | 3224 | 3226 | 3227 | 3228 | 3199 | 3198 | 3197 | 3195 | 3196 | 3191 | 3192 | 3193 | 3194 | 3188 | 3189 | 3187 | 3185 | 3186 | 3183 | 3181 | 3182 | 3179 | 3180 | 3177 | 3176 | 3175 | 3174 | 3173 | 3169 | 3167 | 3164 | 3162 | 3159 | 3158 | 3157 | 3154 | 3155 | 3156 | 3153 | 3149 | 3150 | 3144 | 3145 | 3146 | 3147 | 3148 | 3142 | 3143 | 3139 | 3141 | 3138 | 3136 | 3137 | 3132 | 3135 | 3131 | 3130 | 3127 | 3124 | 3125 | 3126 | 3122 | 3123 | 3121 | 3120 | 3117 | 3119 | 3116 | 3112 | 3113 | 3114 | 3109 | 3110 | 3111 | 3098 | 3099 | 3102 | 3103 | 3104 | 3105 | 3106 | 3107 | 3108 | 3096 | 3094 | 3095 | 3091 | 3092 | 3093 | 3089 | 3090 | 3087 | 3086 | 3082 | 3083 | 3084 | 3080 | 3081 | 3079 | 3078 | 3077 | 3074 | 3075 | 3076 | 3073 | 3072 | 3070 | 3053 | 3055 | 3056 | 3057 | 3058 | 3059 | 3060 | 3061 | 3062 | 3063 | 3064 | 3065 | 3066 | 3067 | 3068 | 3069 | 3052 | 3050 | 3051 | 3048 | 3049 | 3047 | 3044 | 3043 | 3042 | 3041 | 3040 | 3038 | 3039 | 3037 | 3036 | 3035 | 3034 | 3033 | 3029 | 3030 | 3031 | 3023 | 3024 | 3021 | 3022 | 3019 | 3016 | 3017 | 3018 | 3015 | 3012 | 3013 | 3014 | 3011 | 3010 | 3007 | 3008 | 3009 | 3005 | 3006 | 3004 | 3001 | 3002 | 3003 | 2999 | 2995 | 2996 | 2994 | 2991 | 2992 | 2993 | 2990 | 2989 | 2986 | 2987 | 2988 | 2982 | 2983 | 2984 | 2985 | 2979 | 2980 | 2976 | 2977 | 2974 | 2973 | 2970 | 2971 | 2967 | 2968 | 2969 | 2966 | 2964 | 2965 | 2963 | 2961 | 2962 | 2960 | 2958 | 2952 | 2953 | 2954 | 2955 | 2956 | 2950 | 2951 | 2948 | 2949 | 2945 | 2946 | 2947 | 2944 | 2943 | 2939 | 2940 | 2941 | 2942 | 2937 | 2938 | 2936 | 2935 | 2929 | 2930 | 2931 | 2932 | 2933 | 2934 | 2928 | 2927 | 2925 | 2926 | 2921 | 2922 | 2923 | 2924 | 2919 | 2920 | 2917 | 2918 | 2915 | 2916 | 2913 | 2914 | 2912 | 2911 | 2910 | 2909 | 2907 | 2908 | 2906 | 2905 | 2903 | 2904 | 2900 | 2899 | 2898 | 2893 | 2894 | 2895 | 2896 | 2897 | 2890 | 2891 | 2892 | 2887 | 2888 | 2889 | 2885 | 2882 | 2883 | 2884 | 2880 | 2881 | 2878 | 2877 | 2872 | 2873 | 2874 | 2875 | 2876 | 2871 | 2868 | 2869 | 2870 | 2866 | 2867 | 2865 | 2864 | 2862 | 2863 | 2861 | 2860 | 2858 | 2859 | 2856 | 2857 | 2854 | 2855 | 2853 | 2852 | 2848 | 2849 | 2850 | 2847 | 2845 | 2846 | 2843 | 2842 | 2840 | 2841 | 2839 | 2838 | 2837 | 2836 | 2835 | 2833 | 2834 | 2832 | 2831 | 2828 | 2829 | 2827 | 2826 | 2825 | 2824 | 2822 | 2823 | 2820 | 2821 | 2819 | 2816 | 2815 | 2814 | 2813 | 2812 | 2811 | 2793 | 2794 | 2795 | 2796 | 2797 | 2798 | 2799 | 2800 | 2801 | 2802 | 2803 | 2804 | 2805 | 2806 | 2807 | 2808 | 2809 | 2810 | 2791 | 2792 | 2790 | 2787 | 2788 | 2784 | 2785 | 2786 | 2781 | 2782 | 2780 | 2777 | 2778 | 2779 | 2776 | 2775 | 2774 | 2772 | 2771 | 2769 | 2770 | 2768 | 2767 | 2766 | 2764 | 2765 | 2762 | 2763 | 2761 | 2760 | 2759 | 2758 | 2756 | 2752 | 2753 | 2754 | 2755 | 2750 | 2751 | 2748 | 2749 | 2747 | 2745 | 2746 | 2742 | 2743 | 2740 | 2741 | 2739 | 2737 | 2738 | 2736 | 2735 | 2734 | 2733 | 2732 | 2729 | 2730 | 2731 | 2728 | 2727 | 2726 | 2723 | 2724 | 2725 | 2722 | 2719 | 2720 | 2721 | 2718 | 2716 | 2715 | 2714 | 2713 | 2712 | 2711 | 2709 | 2708 | 2706 | 2707 | 2704 | 2705 | 2703 | 2702 | 2700 | 2693 | 2694 | 2695 | 2696 | 2697 | 2698 | 2699 | 2692 | 2690 | 2691 | 2689 | 2688 | 2687 | 2686 | 2685 | 2684 | 2683 | 2680 | 2681 | 2682 | 2678 | 2679 | 2677 | 2676 | 2675 | 2674 | 2673 | 2672 | 2671 | 2670 | 2669 | 2666 | 2668 | 2664 | 2665 | 2662 | 2663 | 2660 | 2661 | 2656 | 2657 | 2658 | 2659 | 2655 | 2654 | 2653 | 2652 | 2649 | 2650 | 2651 | 2646 | 2647 | 2648 | 2643 | 2644 | 2641 | 2642 | 2639 | 2640 | 2637 | 2638 | 2635 | 2636 | 2633 | 2634 | 2631 | 2632 | 2630 | 2629 | 2627 | 2628 | 2624 | 2626 | 2621 | 2622 | 2623 | 2618 | 2619 | 2617 | 2614 | 2615 | 2616 | 2613 | 2612 | 2607 | 2608 | 2609 | 2611 | 2606 | 2605 | 2602 | 2603 | 2604 | 2600 | 2601 | 2599 | 2598 | 2597 | 2595 | 2596 | 2591 | 2592 | 2593 | 2594 | 2585 | 2586 | 2587 | 2588 | 2589 | 2590 | 2584 | 2583 | 2582 | 2581 | 2578 | 2580 | 2576 | 2577 | 2573 | 2574 | 2575 | 2572 | 2571 | 2566 | 2567 | 2569 | 2570 | 2563 | 2565 | 2562 | 2561 | 2560 | 2558 | 2559 | 2557 | 2556 | 2554 | 2555 | 2551 | 2552 | 2548 | 2549 | 2550 | 2547 | 2545 | 2546 | 2542 | 2543 | 2544 | 2540 | 2541 | 2539 | 2537 | 2536 | 2533 | 2534 | 2535 | 2531 | 2532 | 2530 | 2528 | 2525 | 2526 | 2527 | 2522 | 2523 | 2521 | 2519 | 2520 | 2518 | 2517 | 2516 | 2515 | 2514 | 2513 | 2511 | 2512 | 2509 | 2510 | 2508 | 2506 | 2507 | 2505 | 2504 | 2503 | 2502 | 2501 | 2499 | 2490 | 2494 | 2495 | 2496 | 2497 | 2498 | 2489 | 2488 | 2487 | 2486 | 2485 | 2484 | 2483 | 2482 | 2481 | 2479 | 2480 | 2478 | 2474 | 2475 | 2476 | 2477 | 2472 | 2473 | 2471 | 2470 | 2465 | 2466 | 2467 | 2468 | 2469 | 2464 | 2461 | 2460 | 2459 | 2458 | 2457 | 2454 | 2455 | 2456 | 2451 | 2452 | 2453 | 2449 | 2450 | 2447 | 2448 | 2442 | 2443 | 2444 | 2445 | 2446 | 2440 | 2441 | 2439 | 2436 | 2437 | 2438 | 2434 | 2435 | 2433 | 2432 | 2429 | 2430 | 2431 | 2425 | 2426 | 2427 | 2428 | 2422 | 2423 | 2424 | 2421 | 2417 | 2418 | 2419 | 2420 | 2416 | 2415 | 2412 | 2411 | 2410 | 2408 | 2409 | 2407 | 2406 | 2405 | 2403 | 2404 | 2402 | 2401 | 2400 | 2399 | 2398 | 2397 | 2396 | 2395 | 2394 | 2392 | 2393 | 2390 | 2389 | 2387 | 2386 | 2385 | 2384 | 2383 | 2380 | 2375 | 2376 | 2377 | 2378 | 2379 | 2374 | 2373 | 2372 | 2371 | 2369 | 2370 | 2366 | 2368 | 2361 | 2362 | 2363 | 2364 | 2365 | 2360 | 2359 | 2355 | 2356 | 2357 | 2354 | 2353 | 2350 | 2351 | 2348 | 2349 | 2346 | 2347 | 2344 | 2345 | 2343 | 2342 | 2341 | 2337 | 2339 | 2340 | 2335 | 2336 | 2334 | 2333 | 2328 | 2329 | 2330 | 2331 | 2332 | 2327 | 2326 | 2323 | 2324 | 2325 | 2322 | 2321 | 2316 | 2317 | 2318 | 2319 | 2320 | 2314 | 2315 | 2311 | 2312 | 2313 | 2309 | 2308 | 2306 | 2307 | 2304 | 2305 | 2303 | 2299 | 2300 | 2301 | 2297 | 2294 | 2295 | 2296 | 2292 | 2278 | 2279 | 2280 | 2282 | 2283 | 2284 | 2285 | 2286 | 2287 | 2288 | 2289 | 2290 | 2273 | 2274 | 2275 | 2276 | 2277 | 2271 | 2270 | 2269 | 2266 | 2265 | 2263 | 2264 | 2262 | 2260 | 2261 | 2259 | 2258 | 2257 | 2255 | 2256 | 2254 | 2250 | 2252 | 2249 | 2247 | 2248 | 2246 | 2242 | 2243 | 2245 | 2239 | 2240 | 2241 | 2235 | 2236 | 2237 | 2238 | 2234 | 2233 | 2232 | 2231 | 2230 | 2229 | 2225 | 2226 | 2224 | 2222 | 2223 | 2220 | 2221 | 2218 | 2219 | 2216 | 2217 | 2214 | 2215 | 2213 | 2211 | 2212 | 2210 | 2209 | 2208 | 2207 | 2206 | 2205 | 2203 | 2204 | 2202 | 2201 | 2199 | 2200 | 2198 | 2197 | 2195 | 2196 | 2194 | 2192 | 2193 | 2191 | 2189 | 2190 | 2188 | 2186 | 2187 | 2185 | 2184 | 2182 | 2183 | 2180 | 2178 | 2179 | 2176 | 2177 | 2172 | 2173 | 2174 | 2175 | 2171 | 2166 | 2167 | 2169 | 2170 | 2165 | 2156 | 2157 | 2158 | 2159 | 2161 | 2162 | 2164 | 2153 | 2154 | 2155 | 2151 | 2150 | 2148 | 2149 | 2142 | 2143 | 2144 | 2145 | 2146 | 2147 | 2140 | 2141 | 2138 | 2139 | 2136 | 2137 | 2135 | 2129 | 2130 | 2131 | 2132 | 2133 | 2134 | 2128 | 2127 | 2126 | 2125 | 2124 | 2121 | 2122 | 2123 | 2118 | 2117 | 2115 | 2116 | 2114 | 2113 | 2112 | 2111 | 2109 | 2108 | 2107 | 2106 | 2104 | 2105 | 2101 | 2102 | 2103 | 2099 | 2100 | 2096 | 2094 | 2095 | 2093 | 2092 | 2091 | 2089 | 2090 | 2088 | 2087 | 2086 | 2085 | 2084 | 2082 | 2083 | 2081 | 2078 | 2079 | 2080 | 2076 | 2077 | 2073 | 2074 | 2075 | 2071 | 2069 | 2066 | 2067 | 2068 | 2064 | 2060 | 2061 | 2062 | 2059 | 2057 | 2058 | 2052 | 2053 | 2054 | 2055 | 2056 | 2049 | 2050 | 2051 | 2048 | 2047 | 2046 | 2042 | 2043 | 2044 | 2045 | 2040 | 2039 | 2038 | 2036 | 2035 | 2029 | 2030 | 2031 | 2033 | 2034 | 2027 | 2024 | 2025 | 2026 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2016 | 2015 | 2014 | 2013 | 2010 | 2011 | 2012 | 2008 | 2009 | 2007 | 2001 | 2002 | 2003 | 2004 | 2005 | 1993 | 1995 | 1998 | 2000 | 1990 | 1991 | 1987 | 1988 | 1986 | 1983 | 1984 | 1976 | 1977 | 1978 | 1979 | 1980 | 1981 | 1974 | 1975 | 1973 | 1972 | 1970 | 1968 | 1969 | 1967 | 1966 | 1965 | 1964 | 1962 | 1961 | 1959 | 1960 | 1955 | 1956 | 1957 | 1954 | 1952 | 1953 | 1950 | 1951 | 1948 | 1947 | 1946 | 1944 | 1945 | 1940 | 1941 | 1942 | 1943 | 1939 | 1934 | 1935 | 1936 | 1937 | 1938 | 1932 | 1933 | 1931 | 1930 | 1928 | 1927 | 1922 | 1923 | 1924 | 1925 | 1926 | 1916 | 1918 | 1919 | 1920 | 1921 | 1915 | 1914 | 1906 | 1907 | 1908 | 1909 | 1910 | 1911 | 1912 | 1913 | 1902 | 1904 | 1905 | 1895 | 1896 | 1897 | 1899 | 1900 | 1901 | 1891 | 1893 | 1894 | 1890 | 1888 | 1889 | 1887 | 1885 | 1882 | 1883 | 1884 | 1874 | 1875 | 1876 | 1877 | 1878 | 1879 | 1870 | 1871 | 1872 | 1873 | 1868 | 1867 | 1866 | 1865 | 1864 | 1858 | 1859 | 1860 | 1861 | 1862 | 1863 | 1854 | 1855 | 1850 | 1851 | 1852 | 1848 | 1849 | 1846 | 1847 | 1843 | 1844 | 1845 | 1842 | 1831 | 1832 | 1833 | 1834 | 1835 | 1836 | 1838 | 1839 | 1840 | 1841 | 1828 | 1829 | 1830 | 1827 | 1826 | 1825 | 1823 | 1824 | 1818 | 1819 | 1820 | 1821 | 1822 | 1817 | 1815 | 1816 | 1814 | 1812 | 1811 | 1809 | 1810 | 1807 | 1806 | 1805 | 1804 | 1803 | 1802 | 1796 | 1797 | 1798 | 1799 | 1800 | 1801 | 1792 | 1793 | 1794 | 1791 | 1790 | 1789 | 1788 | 1786 | 1785 | 1781 | 1782 | 1783 | 1784 | 1780 | 1779 | 1776 | 1775 | 1772 | 1773 | 1770 | 1769 | 1768 | 1767 | 1763 | 1765 | 1766 | 1762 | 1760 | 1761 | 1757 | 1758 | 1759 | 1755 | 1749 | 1750 | 1751 | 1752 | 1753 | 1754 | 1748 | 1747 | 1745 | 1744 | 1742 | 1743 | 1740 | 1736 | 1737 | 1735 | 1733 | 1732 | 1729 | 1722 | 1723 | 1716 | 1717 | 1718 | 1715 | 1714 | 1712 | 1713 | 1711 | 1710 | 1709 | 1708 | 1706 | 1705 | 1699 | 1700 | 1701 | 1702 | 1703 | 1704 | 1693 | 1694 | 1695 | 1696 | 1697 | 1692 | 1687 | 1690 | 1691 | 1685 | 1686 | 1683 | 1684 | 1682 | 1681 | 1679 | 1677 | 1678 | 1675 | 1674 | 1671 | 1672 | 1669 | 1668 | 1665 | 1666 | 1667 | 1663 | 1662 | 1659 | 1658 | 1657 | 1654 | 1655 | 1656 | 1650 | 1647 | 1648 | 1649 | 1638 | 1637 | 1636 | 1635 | 1628 | 1623 | 1625 | 1626 | 1627 | 1618 | 1619 | 1622 | 1614 | 1615 | 1616 | 1617 | 1613 | 1603 | 1606 | 1607 | 1608 | 1609 | 1611 | 1612 | 1591 | 1592 | 1593 | 1594 | 1595 | 1596 | 1597 | 1598 | 1599 | 1600 | 1602 | 1578 | 1579 | 1580 | 1581 | 1582 | 1583 | 1584 | 1585 | 1586 | 1587 | 1588 | 1589 | 1590 | 1576 | 1577 | 1575 | 1574 | 1573 | 1288 | 1570 | 1565 | 1566 | 1567 | 1568 | 1564 | 1560 | 1559 | 1555 | 1556 | 1557 | 1558 | 1551 | 1553 | 1554 | 1548 | 1549 | 1550 | 1547 | 1545 | 1546 | 1543 | 1544 | 1537 | 1538 | 1542 | 1533 | 1531 | 1529 | 1528 | 1525 | 1526 | 1527 | 1523 | 1524 | 1521 | 1520 | 1517 | 1518 | 1519 | 1515 | 1516 | 1509 | 1510 | 1511 | 1504 | 1505 | 1506 | 1507 | 1508 | 1499 | 1500 | 1501 | 1502 | 1503 | 1497 | 1498 | 1493 | 1494 | 1495 | 1496 | 1489 | 1488 | 1487 | 1485 | 1484 | 1479 | 1481 | 1483 | 1621 | 1477 | 1476 | 1472 | 1473 | 1471 | 1470 | 1468 | 1469 | 1467 | 1454 | 1457 | 1458 | 1459 | 1460 | 1461 | 1462 | 1463 | 1452 | 1451 | 1446 | 1447 | 1448 | 1449 | 1450 | 1442 | 1443 | 1432 | 1435 | 1436 | 1437 | 1439 | 1396 | 1399 | 1401 | 1402 | 1403 | 1404 | 1405 | 1407 | 1408 | 1409 | 1410 | 1411 | 1412 | 1413 | 1414 | 1418 | 1419 | 1420 | 1421 | 1422 | 1423 | 1424 | 1425 | 1426 | 1427 | 1429 | 1430 | 1341 | 1342 | 1343 | 1344 | 1391 | 1392 | 1393 | 1394 | 1339 | 1340 | 1337 | 1329 | 1330 | 1331 | 1332 | 1333 | 1335 | 1328 | 1327 | 1321 | 1322 | 1323 | 1324 | 1325 | 1320 | 1301 | 1302 | 1303 | 1304 | 1305 | 1306 | 1307 | 1308 | 1309 | 1310 | 1311 | 1312 | 1313 | 1314 | 1315 | 1297 | 1298 | 1299 | 1300 | 1291 | 1292 | 1293 | 1295 | 1296 | 1290 | 1280 | 1281 | 1282 | 1285 | 1286 | 1287 | 1279 | 1276 | 1277 | 1278 | 1275 | 1264 | 1265 | 1266 | 1268 | 1269 | 1270 | 1271 | 1272 | 1273 | 1261 | 1262 | 1259 | 1260 | 1257 | 1258 | 1255 | 1254 | 1252 | 1250 | 1249 | 1247 | 1243 | 1244 | 1245 | 1246 | 1241 | 1242 | 1240 | 1238 | 1239 | 1237 | 1236 | 1235 | 1231 | 1232 | 1233 | 1234 | 1228 | 1229 | 1230 | 1224 | 1225 | 1226 | 1223 | 1220 | 1221 | 1222 | 1215 | 1216 | 1217 | 1218 | 1211 | 1212 | 1213 | 1214 | 1209 | 1210 | 1208 | 1202 | 1204 | 1205 | 1206 | 1200 | 1201 | 1199 | 1196 | 1198 | 1192 | 1193 | 1189 | 1190 | 1191 | 1185 | 1178 | 1179 | 1182 | 1184 | 1166 | 1167 | 1168 | 1169 | 1171 | 1173 | 1174 | 1164 | 1163 | 1153 | 1154 | 1155 | 1156 | 1157 | 1158 | 1159 | 1160 | 1161 | 1151 | 1152 | 1147 | 1148 | 1149 | 1146 | 1142 | 1143 | 1144 | 1145 | 1138 | 1139 | 1140 | 1136 | 1133 | 1134 | 1135 | 1132 | 629 | 1130 | 1131 | 1129 | 1123 | 1124 | 1125 | 1126 | 1127 | 1128 | 1122 | 1121 | 1120 | 1119 | 1116 | 1117 | 1118 | 1115 | 1114 | 1108 | 1109 | 1111 | 1112 | 1113 | 1107 | 1106 | 1099 | 1100 | 1101 | 1102 | 1103 | 1098 | 1094 | 1095 | 1097 | 1093 | 1091 | 1092 | 1089 | 1090 | 1088 | 1085 | 1086 | 1081 | 1082 | 1078 | 1079 | 1080 | 1076 | 1077 | 1075 | 1074 | 743 | 1072 | 1073 | 1070 | 1071 | 1069 | 1068 | 1067 | 1057 | 1058 | 1059 | 1060 | 1061 | 1062 | 1063 | 1064 | 1065 | 1066 | 1055 | 730 | 1047 | 1048 | 1049 | 1050 | 1051 | 1052 | 1053 | 1042 | 1043 | 1044 | 1045 | 1046 | 1036 | 1037 | 1038 | 1039 | 1040 | 1041 | 1034 | 1035 | 910 | 1032 | 935 | 1030 | 1031 | 1026 | 1027 | 1028 | 1029 | 1024 | 1025 | 1023 | 1021 | 1022 | 1018 | 1019 | 1020 | 1017 | 684 | 1016 | 1015 | 890 | 1014 | 1011 | 1012 | 1013 | 1010 | 1009 | 1008 | 1007 | 660 | 1006 | 690 | 1005 | 1002 | 1003 | 997 | 999 | 1000 | 1001 | 996 | 995 | 994 | 987 | 988 | 989 | 990 | 991 | 992 | 984 | 985 | 986 | 431 | 983 | 982 | 979 | 980 | 981 | 961 | 977 | 978 | 975 | 976 | 972 | 974 | 969 | 970 | 971 | 968 | 911 | 967 | 817 | 850 | 853 | 658 | | 439 | 966 | 964 | 962 | 963 | 960 | 958 | 959 | 957 | 954 | 955 | 956 | 952 | 953 | 949 | 950 | 951 | 947 | 948 | 946 | 945 | 944 | 943 | 942 | 941 | 938 | 936 | 937 | 934 | 931 | 932 | 933 | 752 | 292 | 815 | 816 | 819 | 316 | 832 | 839 | 846 | 847 | 854 | 855 | 863 | 864 | 865 | 362 | 879 | 888 | 891 | 918 | 689 | 716 | 722 | 724 | 741 | 744 | 746 | 749 | 750 | 929 | 927 | 928 | 925 | 926 | 924 | 153 | 923 | 919 | 920 | 921 | 916 | 914 | 912 | 908 | 909 | 905 | 906 | 464 | 354 | 904 | 878 | 900 | 893 | 894 | 895 | 896 | 897 | 892 | 898 | 899 | 889 | 351 | 885 | 886 | 880 | 881 | 883 | 884 | 667 | 874 | 875 | 361 | 930 | 940 | 430 | 434 | 873 | 825 | 826 | 828 | 829 | 844 | 845 | 849 | 852 | 856 | 857 | 858 | 859 | 860 | 870 | 697 | 764 | 862 | 861 | 818 | 851 | 663 | 830 | 831 | 833 | 834 | 835 | 836 | 838 | 840 | 842 | 843 | 824 | 837 | 822 | 820 | 801 | 810 | 811 | 812 | 814 | 628 | 656 | 657 | 661 | 664 | 665 | 666 | 668 | 669 | 670 | 674 | 675 | 677 | 678 | 680 | 681 | 682 | 683 | 685 | 686 | 687 | 688 | 691 | 692 | 693 | 694 | 696 | 698 | 699 | 700 | 701 | 702 | 703 | 704 | 705 | 713 | 459 | 717 | 719 | 720 | 721 | 725 | 729 | 731 | 734 | 736 | 737 | 740 | 748 | 751 | 754 | 755 | 756 | 757 | 758 | 759 | 760 | 761 | 762 | 711 | 813 | 809 | 808 | 803 | 804 | 805 | 364 | 802 | 800 | 798 | 796 | 797 | 795 | 791 | 792 | 793 | 794 | 461 | 790 | 787 | 788 | 770 | 771 | 772 | 773 | 774 | 775 | 777 | 782 | 784 | 768 | 769 | 767 | 765 | 766 | 626 | 726 | 727 | 728 | 710 | 706 | 295 | 444 | 484 | 652 | 654 | 655 | 643 | 646 | 647 | 648 | 649 | 650 | 630 | 631 | 633 | 634 | 635 | 638 | 639 | 640 | 564 | 578 | 579 | 582 | 583 | 584 | 587 | 588 | 590 | 591 | 592 | 593 | 594 | 595 | 596 | 597 | 598 | 599 | 600 | 601 | 602 | 603 | 604 | 605 | 606 | 607 | 608 | 609 | 610 | 611 | 613 | 614 | 615 | 616 | 617 | 618 | 619 | 620 | 623 | 438 | 442 | 443 | 447 | 448 | 455 | 465 | 466 | 472 | 473 | 481 | 482 | 483 | 576 | 575 | 562 | 532 | 535 | 537 | 539 | 541 | 543 | 545 | 547 | 551 | 553 | 555 | 513 | 514 | 515 | 516 | 517 | 518 | 519 | 520 | 521 | 522 | 523 | 524 | 525 | 526 | 527 | 528 | 530 | 500 | 501 | 502 | 503 | 504 | 505 | 506 | 507 | 508 | 509 | 511 | 487 | 488 | 489 | 491 | 492 | 495 | 496 | 499 | 458 | 456 | 360 | 294 | 293 | 415 | 416 | 404 | 402 | 398 | 401 | 377 | 386 | 372 | 369 | 368 | 358 | 344 | 353 | 355 | 321 | 322 | 325 | 319 | 257 | 8 | 13 | 14 | 271 | 272 | 33 | 289 | 34 | 35 | 296 | 44 | 45 | 86 | 98 | 100 | 106 | 117 | 139 | 145 | 159 | 182 | 183 | 184 | 185 | 210 | 211 | 212 | 216 | 222 | 223 | 235 | 239 | 240 | 243 | 246 | 248 | 250 | 3587 | 3590 | 3160

Start glaze chemistry by learning when you don't need it!

A high feldspar glaze is a good example

This reduction celadon is crazing badly. Why? Its chemistry is dominated by feldspar, which supplies lots of K2O and Na2O fluxes. Scores of recipes being traded online contain 50% or more feldspar; they benefit from these powerful fluxes but inherit their high thermal expansion (COE). Many work only because the body happens to have sufficiently high expansion - often aided by significant residual quartz.

Crazing is more than a cosmetic problem in functional pieces. It reduces ware strength and durability, can compromise food safety and turn into a customer complaint. Let's fix it, starting without chemistry:

A runny, amber, crazed glaze

Related Pictures

A high feldspar glaze is settling, running and crazing. What to do?


Blue glaze with chemistry calculations

This picture has its own page with more detail, click here to see it.

The original cone 6 recipe, WCB, fires to a beautiful brilliant deep blue green (shown in column 2 of this Insight-live screen-shot). But it is crazing and settling badly in the bucket. The crazing is because of high KNaO (potassium and sodium from the high feldspar). The settling is because there is almost no clay in the recipe. Adjustment 1 (column 3 in the picture) eliminates the feldspar and sources Al2O3 from kaolin and KNaO from Frit 3110 (preserving the glaze's chemistry). To make that happen the amounts of other materials had to be juggled. But the fired test revealed that this one, although very similar, is melting more (because the frit releases its oxides more readily than feldspar). Adjustment 2 (column 4) proposes a 10-part silica addition. SiO2 is the glass former, the more a glaze will accept without losing the intended visual character, the better. The result is less running and more durability and resistance to leaching.

Cone 10 mug is crazing after a year. That's OK because it's high-fire, right?


Crazed cone 10R mug

This picture has its own page with more detail, click here to see it.

Wrong. This cone 10R grey stoneware, H550, is OK if the glaze fits. But this high feldspar glaze on the inside has begun to craze after a year. The greyer coloration around the craze lines indicates that water is soaking into the slightly porous body. And, this mug has lost the ring it had out of the kiln. Imagine your customers returning these pieces! Could they be refired to be as good as new? Perhaps. But they would return to this condition. The practical solution is to reformulate this glaze to reduce its thermal expansion.

ChatGPT was completely wrong about the cause of glaze crazing in 2023!


A ChatGPT answer to a question about crazing

This picture has its own page with more detail, click here to see it.

ChatGPT was parroting common wrong suggestions about the cause and solution of the serious issue of crazing. Yet it trained on thousands of internet pages about the subject! Crazed functional ware is defective, and customers will return it. So fixing the problem is serious business, we need correct answers. Consider its suggestions: #1 is wrong. There is no such thing as an "incompatible mix" of ceramic materials. Crazing is an incompatibility in thermal expansions of glaze and body, almost always a result of excessive levels of high-expansion K2O and Na2O in the chemistry of the glaze. The solution is reducing them in favor of other fluxes (the amount per the degree of COE mismatch). #2 is wrong, firing changes don't fix the incompatibility of thermal expansions. #3 is wrong, refiring makes the crazing go away but not the stress of the mismatch, it will for sure return. #4 is completely wrong. Firing higher takes more quartz grains into solution in the melt and should reduce the COE (and mature the body more which often improves fit). And melt fluidity has nothing to do with crazing. Furthermore, if a glaze does not run off the ware, it is not overfired. Of course, this is the worst it will ever be, expect better in future.

High feldspar glazes craze on functional:

Don't put up with it. Fix them.


This picture has its own page with more detail, click here to see it.

This glaze, "Bamboo Cone 10%", contains 50% potash feldspar, so it certainly qualifies as a high-feldspar glaze. K2O and Na2O are thus oversupplied. They have the highest thermal expansions of all oxides, by far. These are needed and valuable, but when grossly oversupplied the result is crazing. This glaze used to work on this body, H550. The previous version of H550 was firing near the bloating point of the body, about 1% porosity, so the recipe had to be changed to provide more margin for error. The new recipe has a more practical 2.0-2.5% porosity; it has no danger of bloating or warping and still has excellent maturity and strength. This glaze was crazing before, and pieces did not leak because the body was dense enough - so they were still watertight. But now it does not work. The solution is to do something that should have been done before: Use a silky matte base recipe that does not craze. I recommend the G2571A base (below right) - the Zircopax, rutile, and iron oxide in the original can be added to it instead.

Craze city: Pure Feldspar and Nepheline Syenite


This picture has its own page with more detail, click here to see it.

These pure material powders were applied to bisque as slurries, suspended by gelling with Epsom salts, and fired at cone 10R. On the left is Custer feldspar on a Grolleg porcelain (P700); on the right is Covia nepheline syenite on a whiteware body (P600).

Feldspars and nepheline syenite supply large amounts of K2O and Na2O, oxides having very high thermal-expansion contributions in glaze chemistry. When these materials are melted essentially by themselves, the resulting glasses have very high thermal expansion relative to typical ceramic bodies - thus the spectacular crazing seen here. Glaze recipes containing high percentages of them can likewise be prone to crazing unless enough lower-expansion oxides, especially SiO2, Al2O3 and MgO, are present.

Links

Glossary Celadon Glaze
A type of stoneware glaze normally fired in a high temperature reduction atmosphere kiln. It is transparent and stained green or blue by the presence of iron oxide.
Glossary Calculated Thermal Expansion
Calculation of the thermal expansion of glazes is a very useful comparative glaze-fit tool. But it’s not a laboratory measurement.
Glossary Limit Recipe
"Recipe logic" is the ability to sanity-check ceramic glaze recipes on sight, by noting that materials present and their relative percentages.
Oxides Na2O - Sodium Oxide, Soda
Troubles Glaze Crazing
Ask the right questions to analyse the real cause of glaze crazing. Do not just treat the symptoms, the real cause is thermal expansion mismatch with the body.
Materials Feldspar
In ceramics, feldspars are used in glazes and clay bodies. They vitrify stonewares and porcelains. They supply KNaO flux to glazes to help them melt.

PayPal
No tracking, No ads, No paywall, No transient content!
Just organized, concise information constantly updated and improved.
Was this helpful? Consider supporting me.

Got a Question?

Buy me a coffee and we can talk

 



https://digitalfire.com, All Rights Reserved
Privacy Policy